From 6ddc9b332dfa1b0f08fdd9e50c7a9b0986fa789d Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Tue, 18 May 2021 19:54:52 +0100
Subject: [PATCH 1/5] Only make Bernoulli cache thread_local if the number type
 looks like it might be variable precision.

---
 .../detail/bernoulli_details.hpp                 | 16 +++++++++++++---
 1 file changed, 13 insertions(+), 3 deletions(-)

diff --git a/include/boost/math/special_functions/detail/bernoulli_details.hpp b/include/boost/math/special_functions/detail/bernoulli_details.hpp
index 7c1141f72..f8d9f873c 100644
--- a/include/boost/math/special_functions/detail/bernoulli_details.hpp
+++ b/include/boost/math/special_functions/detail/bernoulli_details.hpp
@@ -565,11 +565,12 @@ private:
 };
 
 template <class T, class Policy>
-inline bernoulli_numbers_cache<T, Policy>& get_bernoulli_numbers_cache()
+inline typename std::enable_if<std::numeric_limits<T>::digits == 0, bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
 {
    //
-   // Force this function to be called at program startup so all the static variables
-   // get initialized then (thread safety).
+   // When numeric_limits<>::digits is zero, the type has either not specialized numeric_limits at all
+   // or it's precision can vary at runtime.  So make the cache thread_local so that each thread can
+   // have it's own precision if required:
    //
    static 
 #ifndef BOOST_MATH_NO_THREAD_LOCAL_WITH_NON_TRIVIAL_TYPES
@@ -578,6 +579,15 @@ inline bernoulli_numbers_cache<T, Policy>& get_bernoulli_numbers_cache()
       bernoulli_numbers_cache<T, Policy> data;
    return data;
 }
+template <class T, class Policy>
+inline typename std::enable_if<std::numeric_limits<T>::digits, bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
+{
+   //
+   // Note that we rely on C++11 thread-safe initialization here:
+   //
+   static bernoulli_numbers_cache<T, Policy> data;
+   return data;
+}
 
 }}}
 

From a9e5b101207b69dd2d17a384c50f0ea3d3c75061 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 21 May 2021 19:02:16 +0100
Subject: [PATCH 2/5] Correct enable_if's in bernoulli_details.hpp cache
 selection.

---
 .../boost/math/special_functions/detail/bernoulli_details.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/special_functions/detail/bernoulli_details.hpp b/include/boost/math/special_functions/detail/bernoulli_details.hpp
index f8d9f873c..cf3554526 100644
--- a/include/boost/math/special_functions/detail/bernoulli_details.hpp
+++ b/include/boost/math/special_functions/detail/bernoulli_details.hpp
@@ -565,7 +565,7 @@ private:
 };
 
 template <class T, class Policy>
-inline typename std::enable_if<std::numeric_limits<T>::digits == 0, bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
+inline typename std::enable_if<(std::numeric_limits<T>::digits == 0) || (std::numeric_limits<T>::digits >= INT_MAX), bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
 {
    //
    // When numeric_limits<>::digits is zero, the type has either not specialized numeric_limits at all
@@ -580,7 +580,7 @@ inline typename std::enable_if<std::numeric_limits<T>::digits == 0, bernoulli_nu
    return data;
 }
 template <class T, class Policy>
-inline typename std::enable_if<std::numeric_limits<T>::digits, bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
+inline typename std::enable_if<std::numeric_limits<T>::digits && (std::numeric_limits<T>::digits < INT_MAX), bernoulli_numbers_cache<T, Policy>&>::type get_bernoulli_numbers_cache()
 {
    //
    // Note that we rely on C++11 thread-safe initialization here:

From 3685f6d2d24d15b8959748c2066867c8e1a6814e Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sun, 23 May 2021 19:49:34 +0100
Subject: [PATCH 3/5] Update lanczos_generator.cpp: To test over a wider range
 of values, otherwise precision tails off for middling values of z - 100 < z <
 300.  Also prints out conditioning on the near-1 or 2 approximations. Update
 lanczos.hpp with the new approximations, removed 80-100 digit approximation
 because it basically doesn't work well. Modified lanczos.hpp and
 lgamma_small.hpp to have separate lanczos g values for the near 1 or 2
 approximations. This addresses issues discussed in
 https://github.com/boostorg/multiprecision/pull/327.

---
 .../special_functions/detail/lgamma_small.hpp |   10 +-
 .../boost/math/special_functions/lanczos.hpp  | 2223 +++++++----------
 tools/lanczos_generator.cpp                   |   47 +-
 3 files changed, 986 insertions(+), 1294 deletions(-)

diff --git a/include/boost/math/special_functions/detail/lgamma_small.hpp b/include/boost/math/special_functions/detail/lgamma_small.hpp
index a433fbda8..2d5a4b101 100644
--- a/include/boost/math/special_functions/detail/lgamma_small.hpp
+++ b/include/boost/math/special_functions/detail/lgamma_small.hpp
@@ -482,7 +482,7 @@ T lgamma_small_imp(T z, T zm1, T zm2, const std::integral_constant<int, 113>&, c
    return result;
 }
 template <class T, class Policy, class Lanczos>
-T lgamma_small_imp(T z, T zm1, T zm2, const std::integral_constant<int, 0>&, const Policy& pol, const Lanczos&)
+T lgamma_small_imp(T z, T zm1, T zm2, const std::integral_constant<int, 0>&, const Policy& pol, const Lanczos& l)
 {
    //
    // No rational approximations are available because either
@@ -511,16 +511,16 @@ T lgamma_small_imp(T z, T zm1, T zm2, const std::integral_constant<int, 0>&, con
    {
       // special case near 2:
       T dz = zm2;
-      result = dz * log((z + Lanczos::g() - T(0.5)) / boost::math::constants::e<T>());
-      result += boost::math::log1p(dz / (Lanczos::g() + T(1.5)), pol) * T(1.5);
+      result = dz * log((z + lanczos_g_near_1_and_2(l) - T(0.5)) / boost::math::constants::e<T>());
+      result += boost::math::log1p(dz / (lanczos_g_near_1_and_2(l) + T(1.5)), pol) * T(1.5);
       result += boost::math::log1p(Lanczos::lanczos_sum_near_2(dz), pol);
    }
    else
    {
       // special case near 1:
       T dz = zm1;
-      result = dz * log((z + Lanczos::g() - T(0.5)) / boost::math::constants::e<T>());
-      result += boost::math::log1p(dz / (Lanczos::g() + T(0.5)), pol) / 2;
+      result = dz * log((z + lanczos_g_near_1_and_2(l) - T(0.5)) / boost::math::constants::e<T>());
+      result += boost::math::log1p(dz / (lanczos_g_near_1_and_2(l) + T(0.5)), pol) / 2;
       result += boost::math::log1p(Lanczos::lanczos_sum_near_1(dz), pol);
    }
    return result;
diff --git a/include/boost/math/special_functions/lanczos.hpp b/include/boost/math/special_functions/lanczos.hpp
index fbbf447e7..f388cbb27 100644
--- a/include/boost/math/special_functions/lanczos.hpp
+++ b/include/boost/math/special_functions/lanczos.hpp
@@ -69,6 +69,20 @@ struct lanczos_initializer
 };
 template <class Lanczos, class T>
 typename lanczos_initializer<Lanczos, T>::init const lanczos_initializer<Lanczos, T>::initializer;
+
+//
+// Non-member helper which allows us to have a different g() value for the
+// near_1 and near_2 approximations.  This is a big help in reducing error
+// rates for multiprecision types at large digit counts.
+// Default version assumes all g() values are the same.
+//
+template <class L>
+inline double lanczos_g_near_1_and_2(const L&)
+{
+   return L::g();
+}
+
+
 //
 // Lanczos Coefficients for N=6 G=5.581
 // Max experimental error (with arbitrary precision arithmetic) 9.516e-12
@@ -1242,83 +1256,73 @@ struct lanczos24m113 : public std::integral_constant<int, 113>
 };
 
 //
-// Lanczos Coefficients for N=32 G=2.1471552819013595581054687500000000000000000e+01
-// Max experimental error (with 40 digit precision arithmetic) 4.3871855787077623312177313715826599434111453e-39
-// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at Oct 14 2019
-// Type precision was 134 bits or 43 max_digits10
+// Lanczos Coefficients for N=27 G=2.472513680905104038743047567550092935562134e+01
+// Max experimental error (with MP precision arithmetic) 0.000000000000000000000000000000000000000000e+00
+// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at May 23 2021
+// Type precision was 134 bits or 42 max_digits10
 //
-struct lanczos32MP : public std::integral_constant<int, 134>
+struct lanczos27MP : public std::integral_constant<int, 134>
 {
    template <class T>
    static T lanczos_sum(const T& z)
    {
-      static const T num[32] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5570588792269726580426965328821299006241260e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.1774633762992816326945208100096848962840570e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4729248542870148408945035000721777267825674e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.4187209355291098195390045608656819929546438e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.0248306413899929430368029054268103901281039e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.9257678361460200143521812997589499752976231e+40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.6124719365239930504906027891035869583753288e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5454747713027643957043517109001371929077089e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.0864696676761302003121425399683010735367223e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.3986590841584046388095075457448938071498037e+37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.3730272176307717941787236450736722205208718e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.0364763054036420066290166982737191399230330e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5251577656813796428428395564637209124879141e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0012588845037002389721073745460292782912025e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.7802279869271138404361989987596881149322644e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.9402720678039082125732480764868685957396877e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.3191712125257631604053220568076491847333218e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.2201606453728489193256459039591784247070127e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8201383870559727838136908091985005180163020e+26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.5806105013691586921928194185346247254008596e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4998261429327606587262540663611193050275961e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.5175518216952441498193267690845732518664615e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.1558306683405617426954019692046993902758157e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.2526529449739780296036175515849964203851625e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8671408513624251160128760408315369701624440e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.3367482193223363697833634493247948824157616e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.4092037586229976036163287167214501623150351e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.9923609136198492516415716991452463530279321e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.2704580842864713292739934791084236962038214e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.8637257952414489194330242306329389356743799e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.7432900891411285513294395078026439443163899e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.5066282746310005024157652848110452530069853e+00))
+      static const T num[27] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.532923291341302819860952064783714673718970e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.715272050979243637524956158081893927075092e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.399396313336459710065708403038293278484916e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.615805213483907585030394968151583590083805e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.094287593119694642121339924355455488336630e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.985179143643083871895846729884916046817583e+34)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.864723387203319421361199873281888626383507e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.374651939493419385833371654981557918551584e+32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.304504350810987437240912594601486056121725e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.724892917231894382998818728699010291796660e+30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.909901039551708500588401626148435467434009e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.145381204249362220411918333792713760478856e+28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.902980366355225260615014098246446681081078e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.620997933261144559370948440813656891792187e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.003441440382636640319535096309665505136930e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.309721390821762354780404195884829522953769e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.381514076593540726655991152770953882150136e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.275266040978137565809877941293859174071955e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.690398430937632687996992361090819887063422e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.142411407304237744553849404860811146407986e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.174971623395676312463521417132401487856454e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.384092119107453943335286646923309490786229e+12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.296932429990667045419860753608558102709582e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.299378037650538629629318998114044963408825e+07)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.792561328661952922209314899668849919321249e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.580741273679785112052701460119954412080073e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.506628274631000502415765284811045253005320e+00))
       };
-      static const T denom[32] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 0.0000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.6525285981219105863630848000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0596817613895338599493271552000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.9028937852409282099982165606400000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.0707922020245946836608666419200000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5477949752547197371117812531200000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.5189988850542311250318425141248000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.6093078815883681280561453887897600000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.2136536667474513652307465210240000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.3114629767614997850763390570240000000000000e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.4541614716906607001396551577600000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4019376240868075016911422397440000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.2245742324696206305840307600000000000000000e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.0006513636556697864066736800000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4602661104938986779113940000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4256361393293766065270064000000000000000000e+26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.9197210605623737977801375000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.1458832493345014521397750000000000000000000e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.3605580871196332287117500000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.4359416261117272348550000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4960054586805754087500000000000000000000000e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4090257524223082475000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.8433867667953267500000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4097793282984515000000000000000000000000000e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4409270792812500000000000000000000000000000e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.9491892473250000000000000000000000000000000e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1400943144500000000000000000000000000000000e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4803212690000000000000000000000000000000000e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4631225000000000000000000000000000000000000e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0338500000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.6500000000000000000000000000000000000000000e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0000000000000000000000000000000000000000000e+00))
+      static const T denom[27] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 0.000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.551121004333098598400000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.919012881170120359936000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.004801715483511615488000000000000000000000e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.023395306017446756725760000000000000000000e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.087414531983767267719680000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.577035564590760682636262400000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.374646821796792697868000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.144457803247115877036800000000000000000000e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.001369304512841374110000000000000000000000e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.969281004511108202428800000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.188201437529851278250000000000000000000000e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.284218746244111474800000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.805445587427335451250000000000000000000000e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.514594692699448186500000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.557372853474553750000000000000000000000000e+18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.349615694227860500000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.297275331854287500000000000000000000000000e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.956673043671350000000000000000000000000000e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.256393782500000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.968295763000000000000000000000000000000000e+11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.724710487500000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.336854950000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.858750000000000000000000000000000000000000e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.005000000000000000000000000000000000000000e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.250000000000000000000000000000000000000000e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -1326,73 +1330,63 @@ struct lanczos32MP : public std::integral_constant<int, 134>
    template <class T>
    static T lanczos_sum_expG_scaled(const T& z)
    {
-      static const T num[32] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.3676354398462675075959984137356365580662550e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0303243219777652371982632367487187515581930e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.9695330738315109132895792451395673621363046e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.0371873841126513851737915789350097633065208e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.5810211111592336765499877083050083223251925e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.3307571834445765987280306477823996158240302e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.5483950445870222746510194590139013118104375e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.3128221728465167159919234074383914011057504e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.8726824481851158990505892727571391497920715e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1349889148269349577271512140093856701260605e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1228605200219708164439121714303738845598879e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.6361256470584159095341545227609851733775758e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.2166868932853575755146911619588166896783547e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.7377209303689212354445666628772172811909754e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.7350675774071094836814884499810988826239303e+22)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.3912674066825924538916027148038869739001663e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.2420070983154004111449116807024523016395065e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.4700569185690640515452949188152438288912426e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.6124656329989777592191745322776627796111867e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.6406132905056437989704993228158312134178284e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.0968236279962512789710882617045613206867906e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.6644225731453470304909038926424696324288813e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.3859703275819088757835059385783332958674837e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.9272583422150418041465884118526583443207265e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.8348702102467259218213323557081872404861389e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1056941535328594779262418139203368431235554e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1399784061251411774918201133708617903068477e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.4273820161750809875685215118516360445304050e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.0115080627363704378364976159119115750197259e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.7745767713042344487490571988087795152219347e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.2488376091888795863984895909744485000401866e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1860773896913111295543391748504025973928588e-09))
+      static const T num[27] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.630539114451826442425094380936505531231478e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.963898228350662244301785145431331232866294e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.558292778812387748738731408569861630189290e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.438339470758124934572462000795083198080916e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.000511235267926346573212315280041509763731e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.629185970715063928416526096935558921044815e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.237116237146422484431753186953979152997281e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.169337167415775727114018906990954798102547e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.041097534463262894898495303906833076469281e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.981486521549315574859643064948741979243976e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.491567035847004398885838650781864506656075e+18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.093917524216073202169716871304960622121045e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.079147622499629876874169792116583887362096e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.791551915666662583520458128259897770660473e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.834431723470453391466841656396291574724498e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.050635015489291434258728317621551605496937e+11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.715072384266421431637543951156767586591045e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.159505514655385281007353699906486901798470e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.574706336771416438731056639147393961539411e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.488547033239016552342729952719496931402330e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.148012961586177396403312787979484589898276e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.530314564772178162122057449947469958774484e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.370974425637913452858480025228307253546963e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.700056764080375263450528442694493496437080e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.761474446005270789145652778771406388702068e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.889816806780013044430000551700375309307825e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.582468135039046226997146555551548992616343e-11))
       };
-      static const T denom[32] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 0.0000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.6525285981219105863630848000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0596817613895338599493271552000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.9028937852409282099982165606400000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.0707922020245946836608666419200000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5477949752547197371117812531200000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.5189988850542311250318425141248000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.6093078815883681280561453887897600000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.2136536667474513652307465210240000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.3114629767614997850763390570240000000000000e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.4541614716906607001396551577600000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4019376240868075016911422397440000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.2245742324696206305840307600000000000000000e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.0006513636556697864066736800000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4602661104938986779113940000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4256361393293766065270064000000000000000000e+26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.9197210605623737977801375000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.1458832493345014521397750000000000000000000e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.3605580871196332287117500000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.4359416261117272348550000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4960054586805754087500000000000000000000000e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4090257524223082475000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.8433867667953267500000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4097793282984515000000000000000000000000000e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.4409270792812500000000000000000000000000000e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.9491892473250000000000000000000000000000000e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.1400943144500000000000000000000000000000000e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4803212690000000000000000000000000000000000e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4631225000000000000000000000000000000000000e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0338500000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.6500000000000000000000000000000000000000000e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0000000000000000000000000000000000000000000e+00))
+      static const T denom[27] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 0.000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.551121004333098598400000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.919012881170120359936000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.004801715483511615488000000000000000000000e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.023395306017446756725760000000000000000000e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.087414531983767267719680000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.577035564590760682636262400000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.374646821796792697868000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.144457803247115877036800000000000000000000e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.001369304512841374110000000000000000000000e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.969281004511108202428800000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.188201437529851278250000000000000000000000e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.284218746244111474800000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.805445587427335451250000000000000000000000e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.514594692699448186500000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.557372853474553750000000000000000000000000e+18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.349615694227860500000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.297275331854287500000000000000000000000000e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.956673043671350000000000000000000000000000e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.256393782500000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.968295763000000000000000000000000000000000e+11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.724710487500000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.336854950000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.858750000000000000000000000000000000000000e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.005000000000000000000000000000000000000000e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.250000000000000000000000000000000000000000e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -1401,38 +1395,41 @@ struct lanczos32MP : public std::integral_constant<int, 134>
    template<class T>
    static T lanczos_sum_near_1(const T& dz)
    {
-      static const T d[31] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.8968008940705433227909677660515993038374841e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.6618604605116020762015754929520236835404324e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8292545018854689128055824823953561237213555e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.5208766506452851610872857905478685024504482e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.4977346993761774005199362646328436255151093e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.0215319141694562206816207245107490261482447e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.5868485920551737806269221936902170855620396e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.2119342552650938943400026113911660156093453e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.1418202444782049081885117917390551996878611e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.0248307330153472190143848702750491768975848e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8061053255438937388879028538451417962537674e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.2080708594510418170142862951931773430228843e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8014009027542132302057253782788244298905648e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -9.2759167304556987616725030218164051987480377e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.7821648880614102293660548885638379600357589e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.3159048716588863974468231104830412871370083e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.8802059531699177780993451552740605512217594e-09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -6.0864938064916182822437411537845427325953853e-12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.3077465050230400693183749778781074723249743e-15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.4535910089559609770590606433653482492203612e-20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8463914918024931651359730176750702440539677e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.6476799036488876225768641543721151210680141e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.9859528302828214478942827717619270410965131e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.4164337794361162374639737594212065825014909e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.4264219556008516021575829429243024924344353e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -6.3654171220500680155015450276084381767112451e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.1771337070979387873887155215691051891368210e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.6130349210382862255475637378026742528052158e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.0357425223049510242618626197816013695138258e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.2237222565117372586662393874248709023486029e-29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.9653890134419774710417169916706146555543512e-31))
+      static const T d[34] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.264579889722939745225908247624593169040293e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.470545597111704235784909052092266897169254e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.398164226943527197542310295220360303173237e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.166490739555248669771075340695671987349622e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.028101937812836112448434230485371426845812e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -6.003050880354706854567842055875605768028585e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.355206767355338215012383892758889890708805e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -6.173166763225116428638036856999036700963277e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.055748115088123667349396984075505516234940e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.127784364612243323022358484127515048080935e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.013011055366411613813518259345336997226641e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.271137289000937686705998821090835222190159e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.195172534910278451113805217678979457290834e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.421890451863814077221239932785029648679973e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.066311611137421591999312557597869716741027e-11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.797948012646761974584234409950319937184538e-16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.274002995605577985657965320478056380380290e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.270091452696164640108774677242731307730848e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -6.933040546739252731034872986511694993372995e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.405071936614348906224568346156522897751303e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.105092450748689398417350156762592106638543e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.573335807137266819877752062372030042747590e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.690602407074901259448169161354115161602278e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.445091932555604281164557526008785529455861e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.932804556880430674197633802977544778784320e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.320001406610629373227596309759263536640140e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -7.699733918513786660891771237627803608806010e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.776870859236169815307382842451635095251495e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.526154769745297076196084765279504608995696e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.939458578626915680695594094484224178207306e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.229538969055131478930409285699348366508295e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.207569067702627873429089508800955397620386e-23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.542428477414786133402832964643707382175743e-24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.409458057545117569935733339065832415295665e-25))
       };
       T result = 0;
       for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
@@ -1445,38 +1442,41 @@ struct lanczos32MP : public std::integral_constant<int, 134>
    template<class T>
    static T lanczos_sum_near_2(const T& dz)
    {
-      static const T d[31] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.8235732906799716623552488416933899152528589e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.8923760814221749411260475309979161560716608e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5806466857096723284428938485933849993255433e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.0423661676922237999255010522403805001149858e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.8864627302775745934819737805015890258069096e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.4749790611725489418874785394046879079002711e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.2352787155916216728704971718263237763940956e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.0472243539148225143721882968062403836164182e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.5789194097878442125894349247978066638013227e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -8.8554944097961585263202464603716331582929738e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5606436359298279012809323203777498460831161e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.9079793884371809023191793438331090550554931e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5565785753912199592703963702155052413697331e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -8.0152581402976896653242934862478024763161144e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.4040502318727807490297102100258877023641629e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.7293447818191967510645955265996052825799609e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.4887668661450911754046983982188022868005334e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.2592989400365993333512441603746877766052195e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.9941084528494632503325323388230135305735007e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.8483184600922127060811720536956793306527275e-19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.5954546450654998035263505446322855520450213e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.2878426485811911877035106634321308368820032e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.5801420414749176901982573044724995471338101e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.0880244059892646868604082519013410844174147e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.2325617535559095736858057307295434296584568e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.5003147275337403154295953682157801293504851e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.8812468002260686540475204400230633058447779e-26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.8501862565143035234095815929073455137122638e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 8.9497824575117543406738759847704395400692055e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.0574102876284982539299549303708483236373651e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 6.0187464606086614102031360043044718659169199e-30)),
+      static const T d[34] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.391991857844535020743473289228849738381662e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -2.433141291692735004291785549611375831426138e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 5.887812040849956173864447000497922705559488e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -8.178070869177285054991117755136346786974125e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.207850198088647199855281811058606257270817e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.208638257131458956367681504789416772705762e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.651195950543217389263490876246883903526458e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.327903648523876358512872196882929451369963e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.401672908678997114468388150043974540095678e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -7.906706968342945744899907670199667000072243e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 4.916704391410548803397953511596928808893685e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.592256249729202493268939584019491192080080e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.240081857804364904696255913500139170039349e-05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -9.968635402954290441376528527568797927543768e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 7.475731807209447934074840206826861054997914e-11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.961594409606987475034042150632670295904917e-15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -3.697515016601028609216707527257479621172555e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.591523031442252914289458638424672100510104e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -4.860638409502590149748648713304503849363893e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.850723614235842081434077716825371111986246e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.475844999417373489569601576817086030522522e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.804122560714365990744061859839148408328067e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.886336206511766947905039498619940334834436e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.714212931833249115161397417081604581762608e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.355056847554880232469037060291577918972607e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.254308400931922182743462783124793743058980e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -5.398154269396277345367516583851274647578103e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 2.647900793652290520419156346839352858087685e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.069961504286664892352397126472100106281531e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 3.462971538614891132079878533424998572755101e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -8.620091428399885297009840750915836982112365e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 1.547689636281132331592940788973245529484744e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, -1.782453950387991004107321678322483537333246e-23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 134, 9.881473972208065873607436095608077625677024e-25)),
       };
       T result = 0;
       T z = dz + 2;
@@ -1487,9 +1487,14 @@ struct lanczos32MP : public std::integral_constant<int, 134>
       return result;
    }
 
-   static double g() { return 2.1471552819013595581054687500000000000000000e+01; }
+   static double g() { return 2.472513680905104038743047567550092935562134e+01; }
 };
 
+inline double lanczos_g_near_1_and_2(const lanczos27MP&)
+{
+   return 17.03623256087303;
+}
+
 //
 // Lanczos Coefficients for N=35 G=2.96640371531248092651367187500000000000000000000000000e+01
 // Max experimental error (with 50 digit precision arithmetic) 67eps
@@ -1662,41 +1667,49 @@ struct lanczos35MP : public std::integral_constant<int, 168>
    template<class T>
    static T lanczos_sum_near_1(const T& dz)
    {
-      static const T d[34] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.09112391094335813989230740596164619994797033481760301e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.11095925828443504625574261745581427703630213518975734e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.25795762399049096970854782036824945808150003653799701e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.53596813364794430843820749839089482856771473577902136e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.10150518856225197104044336968686219568570379161186763e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.59440015012604275008985164760189204399872934212169290e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.17182126100715726914905437099855137991832224176746144e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.52194070233963020921586697582404279809725757428225907e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.11287192546142126817144783716567250328231623970392395e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.70029010284498269942986238607675315541449827223720491e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.39359986548869257712075354365607803246217579350731025e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.55857186796151318525331772210231419636656738702520247e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.01976508569781091139272219093293962106866776273944401e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.51622799316222576708968190643735578161547893435503117e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 2.55114022296440557292153472011659421232773792851704649e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.29558714084043876803654097222727620781593122323144986e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.20655790191462561334686083455624901268509187198531392e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.29211265190736317625627743320462821391020598683096969e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.16547271274032555838193953745182811226836340887412893e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.04158977282328622262713955181985365200737836471868621e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 9.04099527601588222217706879074903022432460969180041885e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.21026124816545340223909137077288908237190834054935310e-09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.73486546143800890651761116982457576405090186184403710e-12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.92426051924806467732549205594664201603409972582813132e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.61340208721806452778722682494918504979435178283255061e-17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.13517996614037348212434679983945901825382670014683797e-20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.61930266547148210568279523485628689044657261784716591e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.78463508004708787795311937422590618909194917033730955e-31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.53568640059658459444865728826184250691297909350787934e-35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.63117406343686364701920733651409741863929155565374940e-36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.02296711810469513023726896410540806344003955071812851e-36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.05776322342042086937257880311088879198393056129493081e-37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.82527152907979058393765521600344474439209706209233775e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 2.61571352467214817635971061532522193500863154360283722e-39))
+      static const T d[42] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.2258008829795701933757823508857131818190413131511363e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -6.1680809698202901664719598422224259984110345848176138e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 2.0937956909159916126016144892534179459545368045658870e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.2570860117223597345299309707009980433696777143916823e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.7808407045434705509914139521956838552432057817709310e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.5355182201018147597112724614545263772722036922648575e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.8474340895549068665467127190441982794533803160633534e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.9687073432491586288948383529096081854867384409828362e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.4457539281218595159502905008069838638140685905208109e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.0724321926101376768201888687693227423632630755627070e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.1941554220476109189863208161993450668341832413951177e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -6.0469416499468520752326008902894754184436051369514739e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.0254471406496505041361077191383344271915106887055424e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.9743975328123868311047848806382369109187457702980947e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.6326975883294075748535457727960259872733702003969396e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.8276395425975110081829250599527615065306178329307764e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.4994926214942760944619799278085799215984014361562132e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.1685212562684580327244208091708941173130794374261284e-10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.0566129445336641178978472923139566421562362783155822e-13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -6.6744193557172228303189080097715371728193237070211608e-17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.3116377246238995291497495503598572469502355628188604e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.7791795131683583370183641939988202673347172514688534e-28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 9.6372242277604226411817535739257869758194674562641039e-28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.7502495488892655715569603094708394381657045801526069e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.0501577132014302973783965458067331883116843242885033e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.0246214059191840597181314245134333087378581123342727e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.4016071303078853730266134475467378117726380022343630e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.6214830666337247122639245651193515459936309025504988e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.6312853482448038567407561706085851388360060108080568e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.4458785355627609495060506977643541320437284829970271e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.1331287575394227733315016732552406681866623847709417e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -7.8351635033967037250982310034619565150687081453609992e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.7520885958378593874310858129100278585054737696926701e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.5058409122183022757924336573867978222207111500077203e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.1353898614924597482474648262273645405650282912119167e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.3531153377666279783383214654257629384565834244973196e-28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.3839135182642184911017974189326632232475070566724497e-28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.5479558181723745255902653783884759401621303982915322e-29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.0441825447107352322817077249008075090725287665933142e-30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.0157887327297754418593987114368959771100770274203800e-30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 9.4607280988529299025458955706898751267120992042268667e-32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.2702032336418528894772149178970767164510337389404370e-33))
       };
       T result = 0;
       for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
@@ -1709,41 +1722,49 @@ struct lanczos35MP : public std::integral_constant<int, 168>
    template<class T>
    static T lanczos_sum_near_2(const T& dz)
    {
-      static const T d[34] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.27149725743552824677345467452765724462183747425698430e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.29461157973340118022513089366929246812794440622918275e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.12714892558448280578038020250503421879861075137953016e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.78987853703364598882843888232934449281930468883391335e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.61421402429854740596701737352164170551274801368708941e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.35389897687788587032725281528384185518833066402901114e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.02677338784735277115375432621012998338558552597357336e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.26946128083650646734645560602832582368091536233949979e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.62745979285730759140267927796734683888575236461558969e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.98136451866684089001192332403279162096332022571108845e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.61583350640418693864271497678443168377071451407567658e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.98152856924573421857895007425890467500099537012952122e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.18020021813066494304354702578430478815286552616366363e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.76687516020609325102781997617812558189956529947937455e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 2.97286840137911020382328323869139629696357829352821391e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.84037960234558373817068181823488833809395626348103188e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.73663296826451629159939759241902446349258313114071094e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.67102106498038196040637483025426329160024817197530409e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.35813663599770253165594840156807550072235435724240491e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.70970369202279764117806847443483943084782006868895857e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.05355593279987378383061490338957570599931723523376630e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.41032914996100466638712258076005313289749145071459453e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.01788232911919897659739133018267424364933824143275367e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.40766909510419913528326529229511125941552363401838743e-13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.21073243637136845906400015214174112719748429942427344e-16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.32283620509730411652267827642614145629073466029279697e-19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.38291811911040907926983774874091831690977569145002154e-24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -6.74089126429842876230950047383862474772290970041867579e-30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.78955023078122126762117283369038212754061385626732316e-34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.72737133764019622888917725972972138033556721960526187e-35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.35738316863436492576730648996735973692694426493195922e-35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.72855077059130427852097715321796484769785970590691282e-36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.62293563001680479553446157798018614684701661703654843e-37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.04811629504314504274190599430387363985052709041515655e-38)),
+      static const T d[42] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 7.3782193657165970743894979068466124765194827248379940e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.5325256602067816772285455933211570612342576586214891e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.8780522570799869937961476290263461833002660531646012e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.8184384596766268378888212415693303553880671796724735e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.1851863962133477520750252664910607723762372771833722e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -4.9651417912803026185477059393373316779106801664686922e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.4509968222802070571038728168526976259879110509473673e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.7658529366356277958293590921029620586497540226150778e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.6785479743985639684438881535624244315638292743993560e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.8588900406390499925005060563245955316983471925301184e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 3.7619921996662567540276653040387614527561121386327888e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.4238684621351227134322239416053684476498738936970880e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.4045887339956612618258661862314001628281850888893694e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.5648780296066214471224136948413423004282323597057130e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.4644654223878248996887367583334112564695286627087816e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.4332418933955508302078477926243914098802666261366678e-05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.0358676398914795323109452992079597262040795201720992e-07)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.9450781456519433542572418782578042705818718277820822e-09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 2.7416614067965791526251519843473783727166050306987362e-12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -5.9866912469474631311384623900742191091588854047124831e-16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.7643298058164570865040068204832109970445542816595386e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.4928145473701388663847838847907869194628008362147191e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.6442105079571407791997926495585104881317603986245265e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.4668655090053572169091092679046557243825245275372519e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 5.4267531441890485644063141608998212380717408586417687e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -9.1904503977518246823477462773596622658428222241396033e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.2571863845333234910026102012663485977044671519503762e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.4544064381831932921238058900083969277495893492892409e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.4631986986621358205011740516995928067691739105999606e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -1.2968960911316058263225162731552440661464077730310616e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.0163718599154085420173689991270137222141149005433561e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -7.0278330240079354003556694314544898753730575016426382e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 4.2624362787531585897289168590458242934350512724487489e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -2.2476405895248242769628910185593849817270999749433590e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.0183999810930941402072961555627198647985838184285745e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.9045729824028673594421184017022743317479187113896743e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 1.2413159115073860802650598534057774896614268826143102e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.1823766097367740928881247634568036933183255409575449e-28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 6.3183542619623422719031481991659628332908631907371078e-29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -9.1112247985618590949970839428497941653776549519221927e-30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, 8.4859004327675283792859615082199609974336399587796249e-31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 168, -3.8302040910318742925508017945893539585506545571212821e-32)),
       };
       T result = 0;
       T z = dz + 2;
@@ -1757,6 +1778,10 @@ struct lanczos35MP : public std::integral_constant<int, 168>
    static double g() { return 2.96640371531248092651367187500000000000000000000000000e+01; }
 };
 
+inline double lanczos_g_near_1_and_2(const lanczos35MP&)
+{
+   return 22.36563469469547;
+}
 //
 // Lanczos Coefficients for N=48 G=2.880805098265409469604492187500000000000000000000000000000000000e+01
 // Max experimental error (with 60-digit precision arithmetic) 51eps
@@ -2102,10 +2127,10 @@ struct lanczos48MP : public std::integral_constant<int, 201>
    static double g() { return 2.880805098265409469604492187500000000000000000000000000000000000e+01; }
 };
 //
-// Lanczos Coefficients for N=49 G=3.2804746093749997726263245567679405212402343750000000000000000000000000000e+01
-// Max experimental error (with 60-digit precision arithmetic) 88eps
-// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at Oct 14 2019
-// Type precision was 234 bits or 73 max_digits10
+// Lanczos Coefficients for N=49 G=3.531905273437499914734871708787977695465087890625000000000000000000000000e+01
+// Max experimental error (with MP precision arithmetic) 0.000000000000000000000000000000000000000000000000000000000000000000000000e+00
+// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at May 23 2021
+// Type precision was 234 bits or 72 max_digits10
 //
 struct lanczos49MP : public std::integral_constant<int, 234>
 {
@@ -2113,106 +2138,106 @@ struct lanczos49MP : public std::integral_constant<int, 234>
    static T lanczos_sum(const T& z)
    {
       static const T num[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5742499367008530642617319352897520430205552639474773193534726699460038382e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2055424563420473601452029826557352738661904429902299059433513914586136617e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5124573975150897396579361228988665521507891014129938036244581220575769357e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.7657855450073472861630911067774749012357295936579551712546801770340228765e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2200724511833181761435003548793565030399736349888521665887428093215263908e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.6969626159645181170657767707096364240775930310958541253756412108457464465e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1902838064351166646672468793217979804852505454197638767497901741630038659e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.0815524946284433112181691476757266928589723434617417902816279882371678020e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.1085775474754412572785597234367295850853434122501232697548485520290211685e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.0248876219420480494671692552535249842631934230477107608175338135254767453e+69)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.5717898581583284547576613790182065259217990496576104453319232531339965508e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.5987266955225124754687270016251985476100549398788271466921127242855554305e+67)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1277201593916609119851488898621364059725185338025069187337522019022532875e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.3266912844842724918464413240523721967983751112927460422203771012324285814e+65)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.4198349306520385923755583127019190414798256355752152907538684107889754415e+64)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5954968135971263467860541616149005468520952700568675174669869313790120813e+63)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.5697573028906337479684490638442403255222113759866980140004921288934014321e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.2372180596212313667398562038281895205587396825353276904411403952354592724e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.6216537416683580103634264243351068913266542152026155538733152213171424662e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2028581946420676660634538276758371308595650705510961727364638531545389749e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.0668609223671045472881034712995505846341571161239968651357297157517601241e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.9620881267196496193861934343921326919697524102893094861578977849944522047e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.9917155089797622879653341069010820156774380191279115491781432309218621096e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2942244374439765758128985411022615606270110470067503605960457871147797553e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.9351028342882568351470704633625779062510316389795468890729515726996746376e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.9314927110707228066333377498237626208657080992885612416826068446390297282e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.9556005176089621449765653988254594966772984328873034691437246673533838584e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1708002669765411191695114973458120651885979389757503801447241827647515479e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5453624823926493383313636717841737625222638948016893410076575426986147237e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.0870291142516923896770486348199039577071847823857246263136765980806245584e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.3337301613565742543387644582305705841930917569470575861418313137426853827e+40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5696392889303372910143506267477452989689410812923616782357472172107995484e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.4143864855807616500285749805611035801672647319221651520900664580210701417e+37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.3883950248556863481116504212968387826172322376709179509012607292972789664e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.3257340722619328574784440823494550029955992275874284892851081786012219555e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.0054658629154523660536922265411423770787857332470130847913952020455172951e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.2273347597734780854875327656763513602785317406227796368685036961474823856e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.9014441058506987415445336961216002315976811002826148787399813116200761040e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1007719003538290551470147047960192204273669359908829249030378418530058831e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.0380905019192393560853564871253022486270254732200016399586810852416299561e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.9744635849298784873006356360567530952404226257040467086536310864153303851e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1124649237555162417911032704785227088470234269296071198905173077670702197e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.3521744565441850034376761928380748678988834367585778746740882700228177944e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1551192264984335079683102449711150606277601324509245213720618349409077054e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.0649463728846790219460420909345995584550543072052058591106589782466481621e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.8110794685236845669275412185521099716923991533427218655037515888279356458e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.4051945147325155571782612757500183884572379142638708146516926708747795902e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1761279721833493440329993975995822357104129877086617643903445974526391316e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5066282746310005024157652848110452530069867406099383166299235756022800280e+00))
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.019754080776483553135944314398390557182640085494778723336498544843678485e+75)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.676059842235360762770131859925648183945167646928679564649946220888559950e+75)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.735650057396761011129552305882284776566019938011364428733911563803428382e+75)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.344111322348095681337661934126816558843997557802467558098296633193647235e+74)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.279680216265226689865713732197298481387164441051031689408254603978998739e+74)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.534520884978570988754896701605114795240254179745381857143817149573644190e+73)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.094111428842887690996413081740290562974159836498138544655694952917058279e+73)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.810579629726532069935485995735078752851873354363515145898406449827612179e+72)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.558918434547693216059693184449337082460551934950816980580247364223027781e+71)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.135873934032978624782044873078145389831812962597897650459872577452106819e+70)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.371686637133152315568960647279607142944608875215381633194517073295482279e+69)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.210709791290211789451664416279176396010610028867877916229859938579263979e+68)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.728493971517374186383948573740973812742868532549695728659376828743835354e+67)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.082196640005602972025690170863702787506422900608580581233509996818990072e+66)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.434296904963427729210616126543061543796855074189151534322145897294331943e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.956561957668034323532429269801091280845027370525277092791205986418388937e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.088465031117387833989029481250197681372395074774197408003458965955199114e+62)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.638006253255673292005995366039132327048285444095672469721651872147026836e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.251091350064240218784436940525650498454117574503185703454335896105827459e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.438965470269742797671507642697325276853822736866823134892262314489634493e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.171096428020164782492194583597894107448038723781192404665010946856416728e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.967964763783296071512049792468354332039332869323402055488486515880211228e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.691239511306362286583973595898917873397629545053239582674237238671075149e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.371351678345135454487045322888974392983710298168736348320865063481886470e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.399139456864000364822305296187724318277750756512114883045860699513780982e+51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.335644907596902422235465624341780552277299385700659659374735347476790554e+49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.541494306852766687136536628805359613169443442681232300932385167150904206e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.454056970723993494338669836718832149990196703371093557999871225274488103e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.122804036582476347394286398036300142213667443126058369432667730381406969e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.350437044906396962588019269622122085882249454809361766675217669398941902e+43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.350870345849974415762276588597695308720927596639430565914494820338490132e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.751385019528115548010259296564491721747559138159547937603014471132985302e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.476113159838159765344429146854859477076267913220368138623944281045558949e+37)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.294398437121931983845715884547145127710330599817550100565429763115048575e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.839781945206891229035081139535266037057033378415390353746447012903101485e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.711123560991297649877080280435694393772679378388200862936651880878974513e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.629549637595714724789129505098155944312207076674498749184233965222505036e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.574490956477982663124058935512682291631619753616365947349506147258465402e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.813448512582564107136706674347542806763477703915847701777955330517207527e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.794883897023788035285405896000621807947409236640451176090748912226153397e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.960479107645842137800504870276268649357196518321705636965540139043447991e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.584873693858658935208259218348427715203386574579073396812006362138544628e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.245936834930690813978996898166861135901321349975150652784783993349872251e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.773017141345068472510554017030953209437181800565207451480397068178339458e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.641092177320087625773994531564401851985558319657745034892144486195046163e+11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.105900602857710093040451403979744395599050533242553243284994146810134883e+09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.764831079995208797424885873124263386851285031310243195313947355076198006e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.390800780998954208500039666019609185743083611214630479125238184115750385e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.506628274631000502415765284811045253006986740609938316629923576327386304e+00))
       };
       static const T denom[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 0.0000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5862324151116818064296435515361197996919763238912000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1477605944577727245447890951265834050463405543784448000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3368731677410579748749120694395208342752220248276992000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9393177179482022750532799808826502923430631529093529600000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5873212662073383100750664140824866318496576298496819200000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7087596791971826323557398537439095283663043689996772966400000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.8537931401160691803777386867476912131700643521105494016000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7128473077968876977396389430116077066613422855709615718400000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2893230704461912298064838143702096489032830938340968366080000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7731846263715878554484243293204825543527859328977818943488000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.4350612763444239870720412999269509820736318433853587128320000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.0384549286435665533353268142058310243161527793802332119040000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.8399900970142989644612517467287880620408209836099149824000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.3548923093755049924589156254733610823950920495095216128000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.2977252822627446721481004001665655765203461552290590720000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2090496144637581445624377322208214384344648810140669440000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4036595841089057320815648092220077464036379804960768000000000000000000000e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4604307712625044108337677046126892768963323598980608000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3661432041590027825770657688785384893903477321470720000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1520697686278361431114988925105292244781602931070400000000000000000000000e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.7781340723597395269058455794580578514153013123200000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.0542743368034560471670911883883927910588971816800000000000000000000000000e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7852178643724903498642955979619870805662919592000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1476757456360244186066663869698554305163293290000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1067024107708881097170625529475996208174256000000000000000000000000000000e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.1816971152081755906884039315242368042580680000000000000000000000000000000e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2046914254271439983058171150950882746907200000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.5226232704255673172404214340314876574740000000000000000000000000000000000e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9917039581671863252346910306123579600000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.5279926429774219665504424895636324120000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7496375812101278379807519908356136800000000000000000000000000000000000000e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.1781895168846844604663013761970710000000000000000000000000000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.6915825748773446395251490146656000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.5888455419743269266732720488720000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.8324723604341765969313138528000000000000000000000000000000000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1625859075857974372785469560000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7594478264056101488213120000000000000000000000000000000000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3541746402920221829579200000000000000000000000000000000000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7645128331397711271280000000000000000000000000000000000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8231991756227354271000000000000000000000000000000000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.4784681412721648000000000000000000000000000000000000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.8427136416481320000000000000000000000000000000000000000000000000000000000e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1374881704208000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.6720141346000000000000000000000000000000000000000000000000000000000000000e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1948624000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.1833200000000000000000000000000000000000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1280000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0000000000000000000000000000000000000000000000000000000000000000000000000e+00))
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 0.000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.586232415111681806429643551536119799691976323891200000000000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.147760594457772724544789095126583405046340554378444800000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.336873167741057974874912069439520834275222024827699200000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.939317717948202275053279980882650292343063152909352960000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.587321266207338310075066414082486631849657629849681920000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.708759679197182632355739853743909528366304368999677296640000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.853793140116069180377738686747691213170064352110549401600000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.712847307796887697739638943011607706661342285570961571840000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.289323070446191229806483814370209648903283093834096836608000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.773184626371587855448424329320482554352785932897781894348800000000000000e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.435061276344423987072041299926950982073631843385358712832000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.038454928643566553335326814205831024316152779380233211904000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.839990097014298964461251746728788062040820983609914982400000000000000000e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.354892309375504992458915625473361082395092049509521612800000000000000000e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.297725282262744672148100400166565576520346155229059072000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.209049614463758144562437732220821438434464881014066944000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.403659584108905732081564809222007746403637980496076800000000000000000000e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.460430771262504410833767704612689276896332359898060800000000000000000000e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.366143204159002782577065768878538489390347732147072000000000000000000000e+51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.152069768627836143111498892510529224478160293107040000000000000000000000e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.778134072359739526905845579458057851415301312320000000000000000000000000e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.054274336803456047167091188388392791058897181680000000000000000000000000e+47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.785217864372490349864295597961987080566291959200000000000000000000000000e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.147675745636024418606666386969855430516329329000000000000000000000000000e+45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.106702410770888109717062552947599620817425600000000000000000000000000000e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.181697115208175590688403931524236804258068000000000000000000000000000000e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.204691425427143998305817115095088274690720000000000000000000000000000000e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.522623270425567317240421434031487657474000000000000000000000000000000000e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.991703958167186325234691030612357960000000000000000000000000000000000000e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.527992642977421966550442489563632412000000000000000000000000000000000000e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.749637581210127837980751990835613680000000000000000000000000000000000000e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.178189516884684460466301376197071000000000000000000000000000000000000000e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.691582574877344639525149014665600000000000000000000000000000000000000000e+32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.588845541974326926673272048872000000000000000000000000000000000000000000e+30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.832472360434176596931313852800000000000000000000000000000000000000000000e+28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.162585907585797437278546956000000000000000000000000000000000000000000000e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.759447826405610148821312000000000000000000000000000000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.354174640292022182957920000000000000000000000000000000000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.764512833139771127128000000000000000000000000000000000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.823199175622735427100000000000000000000000000000000000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.478468141272164800000000000000000000000000000000000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.842713641648132000000000000000000000000000000000000000000000000000000000e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.137488170420800000000000000000000000000000000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.672014134600000000000000000000000000000000000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.194862400000000000000000000000000000000000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.183320000000000000000000000000000000000000000000000000000000000000000000e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.128000000000000000000000000000000000000000000000000000000000000000000000e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.000000000000000000000000000000000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -2221,106 +2246,106 @@ struct lanczos49MP : public std::integral_constant<int, 234>
    static T lanczos_sum_expG_scaled(const T& z)
    {
       static const T num[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.9156595384723483714761513394165493705512008185104458104037189919966679583e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2490942626049052041642905803851633038401948356209065994820093902482046488e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.5657016133969059292054137486140786946523144967749946090276991389460410256e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.8317575261281828541202228096164333127703313535243593976139496326255603885e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2573232282907489549580534670684496645767812633106925447384772399512629009e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.2264367876545276188760221330510623567338280567044843125670581811561508361e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.7410929642927466039608438519399985289266866350365951941371580436768272283e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1788733746089745519939950216688781077254011132768568000829003039800512115e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7605221646260701306188822826505483714178735327624200723152581930359377597e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2794682649344687478785548483237660272987192396957769664741689026760236827e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5892026994266264487972781655291611074377224857532819461836222961458821278e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.6044581976409422084009086165534449955654966215396670231211076839220955529e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3377067867856641370165698166594859838986332949917530009978864573093452852e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.8840494251009843798733373985085724953611000664053469151896413377742842585e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3704573764322216880093728898018690177362850852138123977146826586562660042e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.0359898089375286965109471568127438755772335943188122764617864358438172366e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.4197682330664983610360781372995395147813463692379312665516728111546651975e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9660635239520142135892297007271080519825235074724441273950199516718744758e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4847561142331378363753305417832438611221296838300212519621989387291450611e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.8123071733863185211372790750342775813125583218947155817719674827525929182e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8695828952857913310728321803468643286198192850402657393713980287261259638e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1112155264857128661506293440611411838336453876178977662636328219208269490e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.9597114546218224309028736968589856884375435031334606638164700453351137400e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2993187112308342042984815542969104496107563160266146124117192158716725839e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.9276492438289459104440745719026053099029450534209231660211458499968839130e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0938880168568707970634270396301729019623679984385010064117584299386152912e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8065713069852021979452626742757704686014267992443726831364663812595589478e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.6307492378187334600766084298235996134621924808224715558467640454423842655e+31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4415490682866089784509877074414842364885644695603000622810515902853301434e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8810050162690958474575145223002401297790616292489104417882204295223485358e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.2860958353933214242194744963395870718749107497800918932121607454081905640e+26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.8895474422826652624342608217034044478811180021465482602156553101973142851e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3673716858987747316948988327383411119224741422002091782489841976044254452e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.9189949269921720477131833122497011042624119182630703457459218878350720360e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.4498506458943304056122167501858896499220570899589497703614276271780187559e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8348122127750881334333964077955476539118633228361300065573128691903485670e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9604661829895068017545272035886457795302072787311442846001622570781400887e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7759001843251065234667097315555616424286286440771094985162292676933917344e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3224448199826427582356965293979283708473565146649764333289536983716495991e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7206022964144885856033111994076522875074747824871090843993137657458226608e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1182242847179807470291498763391918222721736346452719834560856782062915656e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.3003709115482840946768994349442745995208542698397935766566883071074706882e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.0311683127686139178455785110448360190741004055855567244689436514834230540e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2205374026276431316033131273698903101132908812758212963153267146702515001e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.0011852660581895977871209152278420195617235126960126683426738428884540341e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0256927799097601645189517227865464454408483715314872385869625463116763013e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.9285092060573954544191464750091257510108951419853791428165851425157303961e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3651222287552713546296738256776548189076669986821606599921179638781057448e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4196122080178359418232367999588103764109880361922878363699332724809241837e-14))
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.256115936295239128792053510340342045264892843178101822334871337037830072e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.226382973449509462464247401218271019985727521806127065773488938845990367e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.954125855720840120393676022050001333138789037332565663424594891457273557e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.365654586155298475098646391183374531128854691159534781627889669107191405e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.044730374864121201936514442517987939299764008179567577221682561782183421e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.536356651078758500509516730725625323443004425012359430385110182685573948e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.014086778674585662580239648780048641118590040590185584314710995851825637e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.297512615100351568281310997196097430272736169985311846063847409602541101e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.172699484909110833455814713100736399837181820940085502574724938707290372e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.437106278000765568297205273500695563702563420274384149002742312586130286e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.545174371038470657228461270859888251519093095798232203286784662979129719e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.471402006255895070535216946049289412987253853074246902793428565040300946e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.250412452299054568666234182931337401773386777590706330586351790579683785e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.542277292811232416618979097150690892713986488440887554977845301225180167e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.573086578098175124839634461979173468237189761083032074786971884241523043e+49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.104607420271440962257749252277010146224322860594339170999893725175800398e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.331938462909285706991247107187321645123045527742414883815000495606636547e+47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.208943799307442534797422457740696336724404643783689597868534121046756796e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.733493346199244389057953770564978235470425412393741328222813802783023596e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.492565577437473684677047557246888601845840521959370888739670894941330993e+43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.949686666262532681847746981577965659951530620900061798663932175932503947e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.651553737747111429808666993553840522239787479567412806226997545642698201e+40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.233339502372167653077823100186702309252932859938068579827741608727620372e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.836417632015534931979173072268670137192644539820843175043472436022533106e+37)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.099476078371695988128239701316213720767789442435824569996795481661867708e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.903495249944998411669955533495843613032560579446280190215596256375769138e+34)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.064350138053898858268455142115215057417819864153422362951139202939062254e+32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.582922994233975143266417356893351025577967930478759984258796518122317112e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.264234026390622585348908134631186844315412961960282698027228844566912117e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.188774153889105680535092985608022230760508397240005354866271201170463092e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.077355341399798609786211120408446935756994848842131485074396331912972263e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.719182300108746375704686202821491852452619639378413670885143111968297622e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.509589596583338412898049035294868361167322854043341291672085090640104583e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.342872197271389972201661238004898097226547537612646678471852083509061055e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.051089551701679946626603411942133093477647785693757342688765248578133558e+18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.450407423742747934005020832364099630124534867513398798024857849571995697e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.413023778896356322547226273989314105826233010702360664846872922408122652e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.929512168994516762673517469057078217752079550440541815733308359698355209e+12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.122462776963280343259527700358220850883119067227711325233658329309622143e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.197396290684303702682694949348422316362810937601334045965871833844532390e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.356726450420886407112529306259506900505875228060535982041959265851381932e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.263148912218322814862431970673685825699419657740452507847522864799628960e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.320663245567314255422944457710191091603773917350053498982455870821336578e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.270816501767199044429825237923512258332267743288560304635568302760089360e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.960034133400021433681975737071902053498506976351095156717280432287769760e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.650907660437171004901238983264357806498757360812524606971708594836581635e-07)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.725344352001816640635025885398718044955247687225228912342703408863775468e-09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.012213341659767638341287600182102653785253052492980766472349845276996656e-12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.148735984247176123115370642724455566337349193609892794757225210307646070e-15))
       };
       static const T denom[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 0.0000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5862324151116818064296435515361197996919763238912000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1477605944577727245447890951265834050463405543784448000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3368731677410579748749120694395208342752220248276992000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9393177179482022750532799808826502923430631529093529600000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.5873212662073383100750664140824866318496576298496819200000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7087596791971826323557398537439095283663043689996772966400000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.8537931401160691803777386867476912131700643521105494016000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7128473077968876977396389430116077066613422855709615718400000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2893230704461912298064838143702096489032830938340968366080000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7731846263715878554484243293204825543527859328977818943488000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.4350612763444239870720412999269509820736318433853587128320000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.0384549286435665533353268142058310243161527793802332119040000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.8399900970142989644612517467287880620408209836099149824000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.3548923093755049924589156254733610823950920495095216128000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.2977252822627446721481004001665655765203461552290590720000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2090496144637581445624377322208214384344648810140669440000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4036595841089057320815648092220077464036379804960768000000000000000000000e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4604307712625044108337677046126892768963323598980608000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3661432041590027825770657688785384893903477321470720000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1520697686278361431114988925105292244781602931070400000000000000000000000e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.7781340723597395269058455794580578514153013123200000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.0542743368034560471670911883883927910588971816800000000000000000000000000e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7852178643724903498642955979619870805662919592000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1476757456360244186066663869698554305163293290000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1067024107708881097170625529475996208174256000000000000000000000000000000e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.1816971152081755906884039315242368042580680000000000000000000000000000000e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2046914254271439983058171150950882746907200000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.5226232704255673172404214340314876574740000000000000000000000000000000000e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9917039581671863252346910306123579600000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.5279926429774219665504424895636324120000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7496375812101278379807519908356136800000000000000000000000000000000000000e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.1781895168846844604663013761970710000000000000000000000000000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.6915825748773446395251490146656000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.5888455419743269266732720488720000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.8324723604341765969313138528000000000000000000000000000000000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1625859075857974372785469560000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.7594478264056101488213120000000000000000000000000000000000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3541746402920221829579200000000000000000000000000000000000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7645128331397711271280000000000000000000000000000000000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.8231991756227354271000000000000000000000000000000000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.4784681412721648000000000000000000000000000000000000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.8427136416481320000000000000000000000000000000000000000000000000000000000e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1374881704208000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.6720141346000000000000000000000000000000000000000000000000000000000000000e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1948624000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.1833200000000000000000000000000000000000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1280000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0000000000000000000000000000000000000000000000000000000000000000000000000e+00))
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 0.000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.586232415111681806429643551536119799691976323891200000000000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.147760594457772724544789095126583405046340554378444800000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.336873167741057974874912069439520834275222024827699200000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.939317717948202275053279980882650292343063152909352960000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.587321266207338310075066414082486631849657629849681920000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.708759679197182632355739853743909528366304368999677296640000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.853793140116069180377738686747691213170064352110549401600000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.712847307796887697739638943011607706661342285570961571840000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.289323070446191229806483814370209648903283093834096836608000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.773184626371587855448424329320482554352785932897781894348800000000000000e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.435061276344423987072041299926950982073631843385358712832000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.038454928643566553335326814205831024316152779380233211904000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.839990097014298964461251746728788062040820983609914982400000000000000000e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.354892309375504992458915625473361082395092049509521612800000000000000000e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.297725282262744672148100400166565576520346155229059072000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.209049614463758144562437732220821438434464881014066944000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.403659584108905732081564809222007746403637980496076800000000000000000000e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.460430771262504410833767704612689276896332359898060800000000000000000000e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.366143204159002782577065768878538489390347732147072000000000000000000000e+51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.152069768627836143111498892510529224478160293107040000000000000000000000e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.778134072359739526905845579458057851415301312320000000000000000000000000e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.054274336803456047167091188388392791058897181680000000000000000000000000e+47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.785217864372490349864295597961987080566291959200000000000000000000000000e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.147675745636024418606666386969855430516329329000000000000000000000000000e+45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.106702410770888109717062552947599620817425600000000000000000000000000000e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.181697115208175590688403931524236804258068000000000000000000000000000000e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.204691425427143998305817115095088274690720000000000000000000000000000000e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.522623270425567317240421434031487657474000000000000000000000000000000000e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.991703958167186325234691030612357960000000000000000000000000000000000000e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.527992642977421966550442489563632412000000000000000000000000000000000000e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.749637581210127837980751990835613680000000000000000000000000000000000000e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.178189516884684460466301376197071000000000000000000000000000000000000000e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.691582574877344639525149014665600000000000000000000000000000000000000000e+32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.588845541974326926673272048872000000000000000000000000000000000000000000e+30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.832472360434176596931313852800000000000000000000000000000000000000000000e+28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.162585907585797437278546956000000000000000000000000000000000000000000000e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.759447826405610148821312000000000000000000000000000000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.354174640292022182957920000000000000000000000000000000000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.764512833139771127128000000000000000000000000000000000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.823199175622735427100000000000000000000000000000000000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.478468141272164800000000000000000000000000000000000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.842713641648132000000000000000000000000000000000000000000000000000000000e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.137488170420800000000000000000000000000000000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.672014134600000000000000000000000000000000000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.194862400000000000000000000000000000000000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.183320000000000000000000000000000000000000000000000000000000000000000000e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.128000000000000000000000000000000000000000000000000000000000000000000000e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.000000000000000000000000000000000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -2330,54 +2355,54 @@ struct lanczos49MP : public std::integral_constant<int, 234>
    static T lanczos_sum_near_1(const T& dz)
    {
       static const T d[48] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2066789802575522178795921101394468758895980798225454578416417743837821182e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.3679788352265125219923749199991620615257401271523573821302279091870986385e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.2630033804072373059579276357751429378169881873880556882995810292143631169e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.3999752086438541157776701982236284193725611536088710297195418612889088941e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.5326869500703014940743489551921365917396663139743104045090175695793718397e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -9.4539806536100390983482685579769998888148275478188901957443850396223701663e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2418837249375022042463276831798225069762119451024109889652570545798197307e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.2837532371348753406818677898802253115337338144774680681639085300947433821e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0603676137809014970843333435453530863140601935101507289758344098164636049e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.0675156715558786066521224677848991893948220792765278914746791001795702147e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.8231576762102015440131857562883207655276091648820750106248419664382342083e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.6828357670521487851037941818117892204609675060095269337474530867886953446e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.0263919393474265394410446439494942658409182482953883911882462037294240391e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.7511174204844870012138672336839720481677091590654128683087419414952818657e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1077240937707245791059934044373222445269304780721564415689327491376493334e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.7197427650993388314150434222790763404096237849031957731092258677118877326e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1502942251829477374710555866529647619927300737021040120015632037419548655e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.3407293979752550880132165447474755706150471817851620226242890535888257338e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2014334746887994911502478644617408322636134206225589060774099980181312765e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -8.0983646402105726518672426329015155996093741444426226630025345020847577111e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.9942365899792195557178345302806016444352718230344395806792868608352214871e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.3916756170744060855799456788870481671060079696580348774412746337324507629e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.2738029264164285805306112157985005833945884241358728352406636162060451936e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -4.9005795832591317070122324350352498562565929180970558213118848371143071658e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.3120237284050523317140903263269508807725654665206264201337566990649593815e-12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.9993164488488861127293338637233872747923249255635013388317575640760246175e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1770960183589659510713725797228496911736699917131125983799031646762143273e-17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.1067143632180728240506803448567684891294208768806045480286272494772691950e-20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.6244126131167038529019905678720925754781858101865433373489388749513540167e-24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.2602412034992451089948288841723108481473094784377158526788906759478344724e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.5993275050503412644261961442095022244184843038273154020407386192200117900e-35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2376677581089123203915935849311668028430409001498177367770610457728550321e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.8150848887085059253468109780286976776338724012461857375172227849044365287e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.2888861291942792803542790121202831584212092799440963290014968720997192671e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.4367686092860277330824120317504561350242498766190734227637416697402218133e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1658834966582889258321173900424691594425653659844978485212529673045052341e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.6078489664179099912530462853749930668959707942650569176553871936075352345e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0044570187922899426305396174281740469543589839974788550682447627990764739e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.3214978442929458907632954943316397146183013077035413667972521651417588659e-40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.3990788346383540827394552555896039808285381860296208830197355311239959128e-40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -9.1813962257175782149431101470253920074573257556345440519764098954533396958e-41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9566302522237219982311281591833653462640003193980940062047608523626590962e-41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.8844939069206979681852040267695059179818896523029249336074241598129744909e-42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.6980186103098555864348162964443149317288303456071195638226831779183346735e-42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.8409438292612321309493446423416582883045091540877596567806910261300252610e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.4666144269083503254700296220598377304876489203081567665937809718753144311e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.7449599736044707057960973836294763832382889203992176649603299199814964095e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.0585685375038567471031307628591396658405283305367035292669018178549132199e-46))
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.233965513689195496302526816415068018137532804347903252026160914018410959e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.432567696701419045483804034990696504881298696037704685583731202573594084e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.800990151010204780591569831451389602736047219596430673280355834870101274e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.648373417629954217779547889047207255669324591553480603234009701221311635e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.284437059737535030909183878223579768026497336818714964176813046702885009e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.107670081863262975759677889098250504331506870772724719160419469778560968e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.504360049237893454280746661699303420195288960483588101185311510511921407e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.611963690317610801367925234041815344408602188860817148261094946859641055e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.384196825969374886217890731633708081987015968697189525652444057097652970e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -9.622790278065968351142661698209916105231451436587332112667311309898112907e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.449580263451402816852387882691399098166718792531955596134468390704873784e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.521891259305373384442177581056279631601936059906718384076120380236152660e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.540905879286304237452585078525021002948388724011947750659051968465604420e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.945234350579576646146368625320015500721771847656877764914364796999018932e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.387416831492605275144126841246803690906548552137287238128485938487779304e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.495798927786732788454640929952042349030889163403974404914516146280530443e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.422943482445615791699986810123527175351383953692494761445061153868299970e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.102903565532198274392276413606953369815588940855811878456066484772851432e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.094535028891646496546262084074169534843273855151767819779938179094208188e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.358095366769232988323350838247191988585424776577310286935330610243011743e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.340530976890392038064297300042596231921772020705486053763028541479656280e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.516126555541810552632615941497264105370152230590961486150754875983890898e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.581070770182358530034488215134552244420314579258249233845063889274308385e-07)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.004041803560396287949218893554883846494476801309699018606217164405518118e-09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.544940513373792201443764129828570298376651506143103507977578771056330357e-11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.379886756316120706725450388823927894039691498002769785120646242635823255e-13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.045944766231461555774689284231476775257484866624431880423176393512207387e-16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.148008349481903710728852060629194581596537318553456161574664356163226596e-18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.275939213508899016428747078031525836021120921513924955762486505940940452e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.002074313199153828387282409848698339315167131865367803807278126600553143e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.312111841788085794021549817149806212210409562054999023338937587332395908e-31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.626943187621427535665396572257733498961554813667830477603994486170242725e-38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.301342661659868689654008011518619781951990528882947953585638647826710208e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.943206436729179344584590804980950978078020765463364229230497237642990035e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.427985516258891942239250982488681113868086410604389604401061682071089711e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.507315406936486999900039292673781706696418133992677762607195734544800586e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.128602212783277628616662270027724563712726585388232543952969868791288808e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.491772665541813784561971549986243397968726526748411110109050933398474269e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.703534948980953284999107504304646577995487754638088095508324603995172100e-41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -4.254734374358011114570777363031532176229997594050978074992481078060588238e-41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.744400882431682663010546719169103111178937911186079762496396144974231758e-41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.962681142344559707919656870822506290159603512929253279249408502104315114e-42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.676028721091677637759913537058723470799950761402802553076562435074866681e-42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.784145301171889911387402141919770031244273301985414474074193734901497838e-43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.609382025715763421062067113377305459236198785081684246167946524325632358e-44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -8.390549764136377795654766730143252213193890014751189315315457960953487009e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.892571860428412953244204670046307154753124542150699703190076405369134986e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.750996769906711001487027901108989269217518777400665423098451353536180397e-47))
       };
       T result = 0;
       for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
@@ -2391,54 +2416,54 @@ struct lanczos49MP : public std::integral_constant<int, 234>
    static T lanczos_sum_near_2(const T& dz)
    {
       static const T d[48] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5455231550124674608383465879384903101217726809855880053735498558660305251e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.7521171744934997797979463716947798398649024826461953154035391579443199892e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.3025071978608000907597512615615521968983853964414599121560447447486249179e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.0739055847506874449724863962235222139048946552417933333489374601444889442e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.0863054140081769874319573695951392605490718603916106954837774653056576623e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.2108726717088904191265369690298547113580473039391314603986085479556111007e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5906136463190712486212821488571957306185167770225864012898706881699647057e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.6442404200085453327213398272100872399623441451383083438265316066112956103e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3581264998698427315063870744999865373965234956609066658837559718999590062e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -9.0521251281527290170664891261612911437995934455165647349853355253750334406e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.8967279703383588010975605180679227794424995039989024281878608594596616855e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.1553882073152030175586351692198830408611546985761579133373632331779244638e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.7186463308194716629084448574149234823489365098510570780593191406061889318e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.2428438423008152181399734545002360362921592139304278927551479335858821905e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.2612026936693838529789647834479279275034238291000514930718615542291190074e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -9.8875023012785484029602598574637362767234771045911074782572204578687659312e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.4733051533871237880957666174363507890599952187881138769651021452363258297e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.7172158984110335489611392604457344891052843492969255546784144895328933329e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5388046735862609465152559757953131111281278387717331973511139237319990770e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.0372443934101018493930850177650436102881381002613480220638309361418767946e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.1158470789748281012838916430380981653860595791320888251473386188428788856e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.7824681838708087799263224394519010740357745634535755030787340328399772549e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.1931104382411821412587448903202613576618187938526144451753089437172395491e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -6.2766977322268088075311831528842893348256386710249195361734612266778385323e-09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.5228711415779960574453455948991424203497366984285083000319325448210101974e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.5607389508299290889393825247382548268608977769597750095981719736417860627e-13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.3500547558276404981577111880189245551703390604657164900460067017086475257e-16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.9791021994420737378470356651659599587167405408055854179971153565586792084e-19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.2037883058679724499875763987161800762132311085398211645162684109748694340e-23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.6141260374761318937819974670878746263129124551434880143657761001893177100e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.1014080790364138694339981796904397090336135156681914457153169895058123962e-33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.5852138055486955162695207029733124482316515915389725207819834510328826882e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.3247738377057606447050864939101938086522392428747461590714144146282468974e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.9316218892795919921760137631186915684395320376859960566984260379803979907e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.1210308380902232855988541317886447706766253774127605015790322866153349557e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.7740792289514179382145837836403663560484901236914958039358936821942590582e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.0593445713551373294655454085927889987266290706104795764516423812212247302e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.2865158059079907658671256163529513022184187924172645112729579745062723961e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -6.8158128816897517506937531950420472376185024126168447501964316612370015014e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.0727575024490003112672747176557026577347452778581212406977128868690751231e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.1759598612683119428775753540097890056929269067220807101660487076215190882e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.7868733858667171123449703661037140974108364228765817302050018596960416788e-40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.0098516753892371349956889909483048597911093401064123370095186647248754503e-40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.1748345026411581847490576071466694584307900894689508331424519370338054748e-41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.6387013796128814207293408288388785778364579569320260571422484577307186443e-42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.4400648009494470795051094944915668879009266928618607576647564429190022802e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.5157645638963794722990984515235056341682398223940346512667816730324057574e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.3558222299776027787073219176369904651832196778690432544150792644775402371e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.614127734928823683399031924928203896697519780457812139739363243361356121e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.873915620620241270111954934939697069495813017577862172724257417200307532e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.020433263568799913803105156119729477192007677199414299858195073560627451e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.464288862550385816890047588667703388387049707546055857832236105882063068e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.220557255453323997837181773609238378313171107809994660932186398177260086e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.448922988893760252035044756495535237100474172953062930583429032976738764e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.967825884804576295373543809345485166700533400342174877153161242305801190e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.108580240999530194943835615053920860235079936071561387017856553284307741e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.810642568703399030220299393722324927217417866857948859237865608524037352e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.258739608434628125323282855631713548863857229929349389847042534864564944e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 7.128496339139347963949841917163532287235353252857530075762245657435637432e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.298839862995292241245807816785011319551976707839297599695370993581498944e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.248028459892634227909925496833936295152351078572924268478121601580013392e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.852607223132643180520259993802350485519940462836224552121831884016060957e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.663344935420648740647632834149137036410170363282848810726789852512040974e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.956627238308290890004850312580119602770863155061517303602115059073018915e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.169408084580850119987259593698335014334975914638255180200227109093248923e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -4.058851441448441752395908342271882717629330686791993331066549580482119207e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.047904711622988136321913253467026391205138759157051345098701122533901641e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.084581449711468658856874852797634685668605539676219540421511092086784257e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.753524069615947925605286028020036313127948537531901833841745089038345419e-03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.215544327537876774584851905154058374732203881621234998864896154317725107e-05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.068169776809028066872463505146223239383722607505095101927453621607143258e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.929532177536816530254915957100118239727512976366989010196601003141928983e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 4.637071893688824301043677755554700799944720607401583032240419889530137613e-10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.113086368090515818656083953394041201305628629939937324183681568207995992e-12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.052475329075586591944149534403412432330839345810529801140374324740860043e-14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.501688739492061913271178171928421774535209059448213231063121542726735922e-17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 6.901359655394917555561825304708227606591126162154019191593957327845941711e-21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -6.543121984804052902464306048576584437634232699686221158393201347605610557e-25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 5.640594686585611716813857202286477090235259523435190405734068397561049518e-30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.360501538535076761830231649645320930651740695652757112015168140991871811e-37)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.702262550718545671102818966852852449667460777654069395734978498316238097e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -2.541872823365472358451692936741339351955915607098512711275660224596475692e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 3.176003476857354088823169817786505980377842772003301806663816129924483628e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.279773456918425628141724849602711155924011970103858226014129388572719403e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.784385649492108496180681575852127700091310578360977342260193352159187181e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.951360558254817806983487356566692526413661637802019026539779594905551108e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 1.138493498985334706374097781200574458692873800531006014767134080212447095e-39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -5.565540270144127561133019747139820473778629043608866511009741796439135919e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.281818911412862056602174736820614290615384940807745468773991962352596562e-40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -7.799674220733213250330301520376602557698625350979839820580611411813901622e-41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 2.192382536820850868749995412323169490150589703968805623276375892630104761e-41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -4.949971304595638285364920838869349221534754917093372730956379282259345856e-42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 8.645611826340683772044616248727903964535937439036743879074020086333544390e-43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -1.097552479007470044347986004697357054639788223386746160457893283010512693e-43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, 9.016047273189589762707582112298788030798897468010511171850691914431226857e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 234, -3.598528593988298984798384438686079221879557020145063999565131046963034260e-46)),
       };
       T result = 0;
       T z = dz + 2;
@@ -2449,120 +2474,132 @@ struct lanczos49MP : public std::integral_constant<int, 234>
       return result;
    }
 
-   static double g() { return 3.2804746093749997726263245567679405212402343750000000000000000000000000000e+01; }
+   static double g() { return 3.531905273437499914734871708787977695465087890625000000000000000000000000e+01; }
 };
+
+inline double lanczos_g_near_1_and_2(const lanczos49MP&)
+{
+   return 33.54638671875000;
+}
+
 //
-// Lanczos Coefficients for N=49 G=3.71521093750000019895196601282805204391479492187500000000000000000000000000000000000e+01
-// Max experimental error (with 80-digit precision arithmetic) 75eps
-// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at Oct 14 2019
-// Type precision was 267 bits or 83 max_digits10
+// Lanczos Coefficients for N=52 G=4.9921416015624998863131622783839702606201171875000000000000000000000000000000000000e+01
+// Max experimental error (with MP precision arithmetic) 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00
+// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at May 22 2021
+// Type precision was 267 bits or 82 max_digits10
 //
-struct lanczos49MP_2 : public std::integral_constant<int, 267>
+struct lanczos52MP : public std::integral_constant<int, 267>
 {
    template <class T>
    static T lanczos_sum(const T& z)
    {
-      static const T num[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.29576393886533812647621748658593518049105182771886345672193119325886860615058992916e+76)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.64940250521075704286553287922703978233859608760738220959805633167660346858918484441e+76)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.02782279850582131264593341856583603623569135771086732311690891701018783486399941058e+76)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.17871318833644489595452604622172623859528919270761702889241650479860350523603645576e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.24636895901125366174317752785594004344350462222105593541765135970641727807408046603e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.90766536403132277814150094353285923029162708480029761430241108404154368124040257524e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.52382781721986299602475060387708982171655203328511435511051797995280492002324724681e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.78482374388380268613213967834073614067861524793728730151201542394918426634868617345e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.19325027080949586393337406155391099309209314019751861163367432285571050834050337943e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.40545316209557907826875120370637029196186181048557227564363347693674382156389673345e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.45248231502915687322615277256109191586795311001308546524559632502753988355826682144e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.32951710710760475384871665492267398285929602882057694753684715739127717537388087360e+69)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.08609708232067139682194681883946299264352243218047148918541516101215386723695461807e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.96790018517492120048938623906554309076682107791064003018940091271134763465693455777e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.27669033307366420506859833929956397578574575080825866111910129757118415016658467329e+65)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.16802337748974823514819525636942825363065912689755393017268041605495575074123213602e+64)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.73054387508326490801862749035024819220968371854706600225017512476962193917082134622e+63)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.62670382432299595501509896985706425528571034019439577742070022359804568860138431456e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.93419603580003232059946064747952976400826625336761312144282727389088893514776127326e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.64477326525726493380322761443767318183513031346169727378679051953394311858102484110e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.31417565379195208375864005040359979626430954027274059125918083665481151874801228147e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.22873281009357235993917586746434823288058696112725892939606733669981526181084161579e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.24038151344262567906410045463097784963500265667230009248051943941184141216283364012e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.16635103397331843098281133679963613292528445793288854356269441338108669168034969473e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.97226028792130808404381304085761534201244857265870272466382244177818968609788744866e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.51722539705401822010051258989781033530766592277336923172687967760117181597042914505e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.55143196851124103497589961680541188447723645252871343011474640057780989215029733411e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.65631576916353367608977102104279419518759334245125488959476099210969778356845251386e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.51913643147679636800192101181821796326331285929097206716389984328795132228290343736e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.77142070954017798440735921701401232362942654167866941640116269309928860707230400223e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.64265304588830405590756890757870027959619641212378439580733250347485559404826031214e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.12961287129418300922993605074391681508051626956297216905205033442654279681009631622e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.00163852645278376379452857266851549886004284453902427442045925921205957134756527439e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.28416298426892934885339736163488241290345416925540130172490965458139411097784230624e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.49793255972439978183906387866659603599388803095306163216192230005161964280456557158e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.58404837985235629013707612365235872533571223333496498253968477010731743022987544752e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.51210388163173191310089232642285522934883375636207281562370177051035472857070373332e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.29625175202138639315345810129285907904834629385738665013524881366645746417930602439e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.91704411637684940906309546543695853685028152118727394684725500498007979899474115290e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.71980627815396304296720837491060731114276254036666247979635295719640774180255608217e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.99515302992882524356421852289147703799628458429164679118485650618041455793969699036e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.05962638033903929635201902285319054754141795004681756534441119215276710860621598251e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.06860641169958199340995275230206293988239276251216776246763641876943705626715807705e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.34257282855413383182163862298720605042203946165367698145431759335580579509759239742e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.00325103633255410612780052993328410422609156975902055798191507344081921284741604327e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.35516908008075882088679988477934347017452660082246021362543874768562840957846903854e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.05605466237751558310956675128455566243720955874966620350919363272463056561354608608e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.55729572460925281137543520027396380407277254872226907448088245735142585109299314309e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.50662827463100050241576528481104525300698674060993831662992357634350984153163470001e+00))
+      static const T num[52] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.2155666558597192337239536765115831322604714024167432764126799013946738944179064162e+86)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.4127424062560995063147129656553600039438028633959646865531341376543275935920940510e+86)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2432219642804430367752303997394644425738553439619047355470691880100895245432999409e+86)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0716287209474721369403884015994122665163651602768597920624758793936677215462844844e+86)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6014675657079399574912415792629561012344641595734333223485162579517263855066064448e+85)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.9469676695440316675866392095745726625355531618465991865275205877617243118858829897e+84)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.6725271559955312030697432949232367888201769834554225137624859446813736913045818789e+83)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.9780497929717466762906957902715326245615108291247102827737801883575021795143342955e+82)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1101996681004003890634693624249367763382356608502270377869975360325542360496573703e+82)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0730494939748425861290791265310097852481749101609248058586423168275758843014930972e+81)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.1172053614337336389459663390209768009612090987295451850767107564157925998672033369e+79)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.8745706482859815560001340912167784132864948819270481387088631069414787418480398968e+78)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.6357176185157048005266104227745750047123126912102898052446617690907900639513363491e+77)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8133959284164525780065088214012765730887094925955713435258703832914376223639644932e+76)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5448240429477602353083070839059087571962149587434416045281607922549720081768160509e+75)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.7087163798498299832185901789792446192843546181020939291287863440328666852365937976e+73)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.5087881343681529988104227139117041222747015656224230641710513581568311157611360164e+72)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4613990031561986058105893353533330535471171288800176856715938119122276074192401252e+71)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.5842870550209699690118875938391296069620575640884684638841925128818533345720622707e+69)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.9620974233284411294099207169175001352700074635064713292874723705223947089062735699e+68)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.3508670578887212089913735806070046196943428333276779526487779234259460474649929457e+66)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.8965656059697746722951241391165378222796048954133067890004635351203115571283351365e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.2318932193708961851167812069245962898666936025147808964284039760031905048392189838e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3345087899695578368548637479429057252399026780996532026306572668368481753083446035e+62)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1496377806602727082710361157715063723084394483433707624016834119253720339362659524e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.8813988021021593903128761372635593523664342047294885462297735355749747492567917846e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3920956168650489448209669451137968296707297452484593173253158710325555644182737609e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6075799130233642952967048487438119546115615639287311948474085370143960495152991553e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.5215062065032735365892761801093050964342794846560150713881139044884954246649618411e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.2544625196666558309461059934941389307783421507071758131936839820683873609174384275e+51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0762146929190267795931737389984769617036500590695127135611707890269647516827819385e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4748530311527356370488285932357594780386892716488623785717991900210848418789146683e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.8647515097879595082625933421641550420004206477055484917914396725134286781971556627e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1719649433541326415406560692060639805792580579388667358862336598215919709516402950e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.3261545166351967601378626266818200343311913249759151579277193749871910741821474852e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2856597199911108057679518458817252978491416960383076400280909448497251424577297828e+40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0550442252418806202988575468283015522717243147245311227478147425985867569431393246e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6853992677311201643273807677942992750803865734634293875367989072577697582186788546e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2561436609157539906689091056055983931948431067099841829117491622768568140084478954e+34)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.4705206401662673954957473131998048608819946981033942322942114785407455940229233196e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.1407133281903210341367420024686210845937006762879607281383052013961468193494392782e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.7901285852211406723998154843259068960125192963338996339928284868353890653815257694e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3438998631585891046402379167404007265944767353624748363650936091693896699924614422e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.6902706401090767936392657986442523138728548699749092883267263725876049498265301615e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0929659841192947874271802260842934838560431084502779238527946412041140734245143884e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.5862712170406726646812829026907981494912831615106789457689818325123973212320279526e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7379005522986464990683100411983090503131358664627225315444053238030719367736285441e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.7401492854176051649551304067922101744785432102294852270917872876250420006402939364e+12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.3052097444388598287826452442622724171650622602495079541553039504582845036611195233e+09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.8093796662195533917872631136981728293723308532958487302137409818490410036072819019e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.3192906485096381210566149918556620595525679738152760526187454875638091923687554946e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.5066282746310005024157652848110452530069867406099383166299235763422936546004304390e+00))
       };
-      static const T denom[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.58623241511168180642964355153611979969197632389120000000000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.14776059445777272454478909512658340504634055437844480000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.33687316774105797487491206943952083427522202482769920000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.93931771794820227505327998088265029234306315290935296000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.58732126620733831007506641408248663184965762984968192000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.70875967919718263235573985374390952836630436899967729664000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.85379314011606918037773868674769121317006435211054940160000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.71284730779688769773963894301160770666134228557096157184000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.28932307044619122980648381437020964890328309383409683660800000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.77318462637158785544842432932048255435278593289778189434880000000000000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.43506127634442398707204129992695098207363184338535871283200000000000000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.03845492864356655333532681420583102431615277938023321190400000000000000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.83999009701429896446125174672878806204082098360991498240000000000000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.35489230937550499245891562547336108239509204950952161280000000000000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.29772528226274467214810040016656557652034615522905907200000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.20904961446375814456243773222082143843446488101406694400000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.40365958410890573208156480922200774640363798049607680000000000000000000000000000000e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.46043077126250441083376770461268927689633235989806080000000000000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.36614320415900278257706576887853848939034773214707200000000000000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.15206976862783614311149889251052922447816029310704000000000000000000000000000000000e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.77813407235973952690584557945805785141530131232000000000000000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.05427433680345604716709118838839279105889718168000000000000000000000000000000000000e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.78521786437249034986429559796198708056629195920000000000000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.14767574563602441860666638696985543051632932900000000000000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.10670241077088810971706255294759962081742560000000000000000000000000000000000000000e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.18169711520817559068840393152423680425806800000000000000000000000000000000000000000e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.20469142542714399830581711509508827469072000000000000000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.52262327042556731724042143403148765747400000000000000000000000000000000000000000000e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.99170395816718632523469103061235796000000000000000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.52799264297742196655044248956363241200000000000000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.74963758121012783798075199083561368000000000000000000000000000000000000000000000000e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.17818951688468446046630137619707100000000000000000000000000000000000000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.69158257487734463952514901466560000000000000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.58884554197432692667327204887200000000000000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.83247236043417659693131385280000000000000000000000000000000000000000000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.16258590758579743727854695600000000000000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.75944782640561014882131200000000000000000000000000000000000000000000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.35417464029202218295792000000000000000000000000000000000000000000000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.76451283313977112712800000000000000000000000000000000000000000000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.82319917562273542710000000000000000000000000000000000000000000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.47846814127216480000000000000000000000000000000000000000000000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.84271364164813200000000000000000000000000000000000000000000000000000000000000000000e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.13748817042080000000000000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.67201413460000000000000000000000000000000000000000000000000000000000000000000000000e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.19486240000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.18332000000000000000000000000000000000000000000000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.12800000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
+      static const T denom[52] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.0414093201713378043612608166064768844377641568960512000000000000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3683925049359750564345782687270252191318781054337155072000000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8312047394413543873001574618939688475496532684433218600960000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.6266290361540649084000356943724186480051615706407501824000000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2578261522689833134479268958172001145701798207577980403712000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2001844261052005486660334218376501837226733355004196185702400000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1681037008119350981332433342566749327534832358109654944841728000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.0293361153311185534392570196926631029364162024577328008396800000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7968291458361430782020246122299560311802074147902210076049408000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.4212998306869600977887871207212578754682594793002122395254784000000000000000000000e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4006322967557247180769968530346138316658911433773347563153653760000000000000000000e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1334912462852682149761710693821775975226278702191992823808000000000000000000000000e+62)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.1263921790865468343839418571823409266633338824655665334886400000000000000000000000e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0548002159482240692664043366538929906734975613031337827840000000000000000000000000e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6095781466700764043324234378972985924892034584990590768742400000000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1887214284827766716471402753528692603931747042835394432000000000000000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6644926572075096083148238618984385847884240529010940198400000000000000000000000000e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9154102380883742873084802432628398856163736124576909120000000000000000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8768151045628896730547232493410634338494669305466040192000000000000000000000000000e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.5674503027583263140245049650089911892130421780961760000000000000000000000000000000e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0774565729992714117801952876016228015049549176491224000000000000000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5271995659293168127377699172748774995796493494870600000000000000000000000000000000e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0217297271367563021376459886512004721472442416486880000000000000000000000000000000e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.2295402510227377004563262212164474005108576587500000000000000000000000000000000000e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.4652078765044198452095090589463630638929867781650000000000000000000000000000000000e+49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7599751702378955591170076678443001141850220448750000000000000000000000000000000000e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.1661954970720573655661780303655361431161958585000000000000000000000000000000000000e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.4624589782073664468902246801624082962588775000000000000000000000000000000000000000e+45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3415303241063823936930939721131813816093940000000000000000000000000000000000000000e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.7484118887814252101652801793318408875609500000000000000000000000000000000000000000e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5345701242523770267594030980609724717749800000000000000000000000000000000000000000e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.5242293875075726230709587746676742825000000000000000000000000000000000000000000000e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2153799706792737162996155167868591485000000000000000000000000000000000000000000000e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9704836232659058554494106146940431250000000000000000000000000000000000000000000000e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.5926306456751344865378122278650335000000000000000000000000000000000000000000000000e+34)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3255133142885196993084362383550000000000000000000000000000000000000000000000000000e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.4074634262098477202456261501600000000000000000000000000000000000000000000000000000e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9362537824702021303895557050000000000000000000000000000000000000000000000000000000e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.7695574975175958167624223800000000000000000000000000000000000000000000000000000000e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.5430949131153796097540000000000000000000000000000000000000000000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.7427444047045863749135000000000000000000000000000000000000000000000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.9163115009072256171250000000000000000000000000000000000000000000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.9274383168492884295000000000000000000000000000000000000000000000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.0731790610548750000000000000000000000000000000000000000000000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9491312919646000000000000000000000000000000000000000000000000000000000000000000000e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1366198225750000000000000000000000000000000000000000000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.3570498490000000000000000000000000000000000000000000000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1862250000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.9135000000000000000000000000000000000000000000000000000000000000000000000000000000e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2750000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -2570,107 +2607,113 @@ struct lanczos49MP_2 : public std::integral_constant<int, 267>
    template <class T>
    static T lanczos_sum_expG_scaled(const T& z)
    {
-      static const T num[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.49663610130791477461794140374370924490696733744664264226063545477852907120064438588e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.20884482942845999689198014205795770851399772847436497410154319183860398480228326286e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.53289916571146966947513241858798999095967787802671792160665282347073321227016292403e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.06257315326410705497495763375336857281692495321204603919284336971479478405381409540e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.13462097275260056500457419367381935327442299676685171001942731892832408882413435566e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.13102394952914002112762425649207244062991186339070382885956481064589709031894816496e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.04840581629048620249901745346405131124091439055732548308528857701167494671648257347e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.43838524961944675350746734141447316445830054880306039896637689653198992735066081474e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.74531483688910159100344151068655208511626316424159676205726034341092475816888011372e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.03005469109920428385867124264753643595038929217266678155910599078268836953793159656e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.06452229265586101928934888140259774581544836837635812825070642317924068191237940651e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.74401260751298616807064335204160985098707747263556384563576228484205922370857356950e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.95999059097413995107763881990067736638605879036860399501004480843044798852321320153e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.83966309607370356019329894907872727851559431468853382195539375506355518522739451561e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.86727909378079977412627692901220876068535926169729765468023963613209750668440883454e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.32183997980385285815563935626564558737112327901896765866420315909089479889407291483e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.26831322790199691523763382147990685271332413931335425536077401693909941536685446004e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.32249937786475248948857177694117967417864070990756190329454700663693499608768713815e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.88336686819032307424839603734550094343459546588744595045643380205822126447806151375e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.20545206582813581050133859680698140274276251798965738445951215893805514854794850980e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.62765065960304045423639870153223988753806599339881709607153712409175486794708548715e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.63343521375027791107490012004281169470903074417529835343633992756599689706467597925e+40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.30646566133119269769508008116142168214781437395136629206311256865360022042754477332e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.58771569575797497748917749020901655508364490119697350339089287796185236358536233400e+37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.37706135782308791418825498038425839394113136784263252755599976807797063043875082698e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.11197240850069894333209760920904406397403024207197696391699562264322296386093323413e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.60283960927607800898139439849090533043340726395143638152077844277751805149166560973e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.61130330576422804633963440554474730419413739922460725405112412454286488484955915987e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.11337300300297295349076762512699923957438723580465440290334845396273762855836733517e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.03117042948259288566605349078528499682057378893001882806984505986948136392761267006e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.40259403730882930955675549420130062238621449273398874217078083754343032954759973357e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.22528347572098799721775967384397848588784390912022136506439711506219967445623919686e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.34099499566403754037791880900467520578107411723617564672664393961433945628291065109e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.41161286449337414692992004461766142962293572495919749372515938105183883550234862604e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.09783271453440804906045665973485276329744852249747400433246982560607811629926185500e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.16094688076417849092104554198103013111536406662498981965117749909832209236913802539e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.10821885688578986410930893219376699456504867926107715594671444282949767588694287037e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.50021127722497072888981489155684575207215375480643952454970468046331143014884622646e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.26818800470068614566377728536610325478326870447541587095650095821101649087210816040e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.92493678677258766132448688907920434402513619957710479626424529957236460471189038381e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.92804216541904692956935385209461325937556277824668580633404375808334363503194457710e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.50949734377247428538055873924894146321959030826140132714559567319426159642629912422e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.64636917688205569668044105440719648394808067896062765005278597960400006426062506946e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.44976703261974330359141562652121211268881081847095890846270752149427888286399621821e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.35281305841345486358892992557075736755186129730528304574018484234880523171404766251e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.72610018227274377132777187985570646349538821991325846732587180123971090415405994340e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.97267688814850268231161594533176277702963907108885229111755006417082297177116403628e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.34003577384307789433517516041141801840291757339440089597599691127216013708701908122e-13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.83710441782049075320423070384744844199992659460213011403809803120117400852034616312e-16))
+      static const T num[52] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2968364952374867351881152115042817894191583875220489481700563388077315440993668645e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3379758994539627857606593702434364057385206718035611620158459666404856221820703129e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.7667661507089657936560642518188013126674666141084536651063996312630940638352438169e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2358817974531517479015567958773172164495426366469934483861648449503257164430597676e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.4277884337482721045863559292777143585727342521289738221346249419373476553706960477e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0321517843552558179026592998573667333331808062275687745076218349815677074985963362e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6008215787076020416349896191435806440785263359504290408274535992043818825469757467e+62)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0818534880683055883178218002277669005830432150690130666222387190067193078388546735e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.3163575041638782544481444410280012073460223217514438140658322833554580013590099428e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2388461455413602821779255933063678852868399289922539164611151211712717693487661387e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.9022440433706121764851738708000810548525373575286185895490944900856672029848122464e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4343332795539887118781806263726922877784774015269102474184340994778721415926159254e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.6721153873219058826376914786734034750310419590675042405183247501763477751707551977e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.8699628167986487178009534272364155924157279822557444996249799757685987843467799627e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2231722520846745745100754786781488061001048923809737738337722261187091800649653747e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6083722187098822924476598339806607838145759265459316214837904824198871273160389130e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.3208522386531907691637761481331075921814846045082743370064300808114976199945037122e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.0491114749931089548713463433723654679587396917777106103842119656518486449033314603e+49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1651242201716492163343440840407055970036142959703118121095709130441296636187948680e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.0937853081905503955154539906393844955264076759979726863680373891843152853217317289e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3250660210211249438634406634827812076838178133500698949898645633350310552370070845e+45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9570575453729198045577937136948643736522682229986841993417806493265120889607818521e+43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0915995985127530070498760979124015775616748288243587047367665303776535820627821806e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.7843635148151485646319955417265990806303645948936943738048724343049029864512194310e+40)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.5715089981189796608580098957107087883056675964697423692398096552244865201126563742e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4357579282713452366310121777478478833619311278663562587227576970753556113485917320e+37)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9045145853415845950075255530781663873014618840017618405203106705648527948595759022e+35)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.4405414384364870662900944749199576151689786973539596080446881216688775114111401244e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.4338208995125086931437020109275839003754703899452696411395381222142064582727164193e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5135951828248789401437398422210292739440102976394266807495518051141687446206426902e+30)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2454501218684993019799803589484969919745689383924985827556442495293105857928357346e+28)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.0771824063818140076215034706980442595962662610399835096143334152833816531221628660e+26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.8906795572088352821870480514365587413988764084322141604846302060067104077934035979e+24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.5316598805398286987903918997966274192433403859480290402541541527289805994033568970e+22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.8533661333839969582529636915290426021792269810841946250308753325085094758818317464e+20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.7688764431225908123092120518561018783609436337842987641148647520393460757258932651e+18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.2877126063932361367573287637428749753108811218139980724742491890986894871059180965e+16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.5164730755154849065370365582371664006783859248354506763822538105452920154803662025e+14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6208599037402680475080806960664748732421517587082652352333314249266933718172853538e+12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7673175927530323929887314159232706831613273850912577130092484125942772196619237882e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0725755228231653548395606930605822556041123469753556193146323302002970112193491322e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.8214170582643892131251904381692606071847290625764371754232909841174413907293095377e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8039573621910762166001861467061356387294777080327106241940313632291985560896860294e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1872369877837204032074079418146123055615124618000942960799358353269625124323889098e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.3668338250989578832466315465536077672534713261875481920848252453271529995224516632e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3741815275584317532245789502116967720634823787379160467839166784058598703361284195e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.6260135014231198723283200126807995474827979567257597700738272144468899515236872878e-07)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.8035718374820798318368374097127140964803349360705519156103446564446533105562174708e-10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3155399273220963343988533731471377905809634204429087235409329216539588313353641052e-12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6293749415061585604836546051163481302110136557722031417335367202114639560092787049e-15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3184778139696006596104645792244972612333458493576785210966728195969324996631733257e-18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.2299125832253333486600023635817464870204660970908989075481425992405717273229096642e-22))
       };
-      static const T denom[49] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.58623241511168180642964355153611979969197632389120000000000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.14776059445777272454478909512658340504634055437844480000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.33687316774105797487491206943952083427522202482769920000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.93931771794820227505327998088265029234306315290935296000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.58732126620733831007506641408248663184965762984968192000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.70875967919718263235573985374390952836630436899967729664000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.85379314011606918037773868674769121317006435211054940160000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.71284730779688769773963894301160770666134228557096157184000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.28932307044619122980648381437020964890328309383409683660800000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.77318462637158785544842432932048255435278593289778189434880000000000000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.43506127634442398707204129992695098207363184338535871283200000000000000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.03845492864356655333532681420583102431615277938023321190400000000000000000000000000e+57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.83999009701429896446125174672878806204082098360991498240000000000000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.35489230937550499245891562547336108239509204950952161280000000000000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.29772528226274467214810040016656557652034615522905907200000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.20904961446375814456243773222082143843446488101406694400000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.40365958410890573208156480922200774640363798049607680000000000000000000000000000000e+53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.46043077126250441083376770461268927689633235989806080000000000000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.36614320415900278257706576887853848939034773214707200000000000000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.15206976862783614311149889251052922447816029310704000000000000000000000000000000000e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.77813407235973952690584557945805785141530131232000000000000000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.05427433680345604716709118838839279105889718168000000000000000000000000000000000000e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.78521786437249034986429559796198708056629195920000000000000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.14767574563602441860666638696985543051632932900000000000000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.10670241077088810971706255294759962081742560000000000000000000000000000000000000000e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.18169711520817559068840393152423680425806800000000000000000000000000000000000000000e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.20469142542714399830581711509508827469072000000000000000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.52262327042556731724042143403148765747400000000000000000000000000000000000000000000e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.99170395816718632523469103061235796000000000000000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.52799264297742196655044248956363241200000000000000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.74963758121012783798075199083561368000000000000000000000000000000000000000000000000e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.17818951688468446046630137619707100000000000000000000000000000000000000000000000000e+33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.69158257487734463952514901466560000000000000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.58884554197432692667327204887200000000000000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.83247236043417659693131385280000000000000000000000000000000000000000000000000000000e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.16258590758579743727854695600000000000000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.75944782640561014882131200000000000000000000000000000000000000000000000000000000000e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.35417464029202218295792000000000000000000000000000000000000000000000000000000000000e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.76451283313977112712800000000000000000000000000000000000000000000000000000000000000e+21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.82319917562273542710000000000000000000000000000000000000000000000000000000000000000e+19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.47846814127216480000000000000000000000000000000000000000000000000000000000000000000e+17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.84271364164813200000000000000000000000000000000000000000000000000000000000000000000e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.13748817042080000000000000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.67201413460000000000000000000000000000000000000000000000000000000000000000000000000e+10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.19486240000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.18332000000000000000000000000000000000000000000000000000000000000000000000000000000e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.12800000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
+      static const T denom[52] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.0414093201713378043612608166064768844377641568960512000000000000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3683925049359750564345782687270252191318781054337155072000000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8312047394413543873001574618939688475496532684433218600960000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.6266290361540649084000356943724186480051615706407501824000000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2578261522689833134479268958172001145701798207577980403712000000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.2001844261052005486660334218376501837226733355004196185702400000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1681037008119350981332433342566749327534832358109654944841728000000000000000000000e+65)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.0293361153311185534392570196926631029364162024577328008396800000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7968291458361430782020246122299560311802074147902210076049408000000000000000000000e+64)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.4212998306869600977887871207212578754682594793002122395254784000000000000000000000e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4006322967557247180769968530346138316658911433773347563153653760000000000000000000e+63)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1334912462852682149761710693821775975226278702191992823808000000000000000000000000e+62)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.1263921790865468343839418571823409266633338824655665334886400000000000000000000000e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0548002159482240692664043366538929906734975613031337827840000000000000000000000000e+61)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6095781466700764043324234378972985924892034584990590768742400000000000000000000000e+60)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1887214284827766716471402753528692603931747042835394432000000000000000000000000000e+59)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6644926572075096083148238618984385847884240529010940198400000000000000000000000000e+58)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9154102380883742873084802432628398856163736124576909120000000000000000000000000000e+57)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.8768151045628896730547232493410634338494669305466040192000000000000000000000000000e+56)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.5674503027583263140245049650089911892130421780961760000000000000000000000000000000e+55)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0774565729992714117801952876016228015049549176491224000000000000000000000000000000e+54)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5271995659293168127377699172748774995796493494870600000000000000000000000000000000e+53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0217297271367563021376459886512004721472442416486880000000000000000000000000000000e+52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.2295402510227377004563262212164474005108576587500000000000000000000000000000000000e+50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.4652078765044198452095090589463630638929867781650000000000000000000000000000000000e+49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.7599751702378955591170076678443001141850220448750000000000000000000000000000000000e+48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.1661954970720573655661780303655361431161958585000000000000000000000000000000000000e+46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.4624589782073664468902246801624082962588775000000000000000000000000000000000000000e+45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3415303241063823936930939721131813816093940000000000000000000000000000000000000000e+44)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.7484118887814252101652801793318408875609500000000000000000000000000000000000000000e+42)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.5345701242523770267594030980609724717749800000000000000000000000000000000000000000e+41)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.5242293875075726230709587746676742825000000000000000000000000000000000000000000000e+39)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2153799706792737162996155167868591485000000000000000000000000000000000000000000000e+38)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9704836232659058554494106146940431250000000000000000000000000000000000000000000000e+36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.5926306456751344865378122278650335000000000000000000000000000000000000000000000000e+34)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3255133142885196993084362383550000000000000000000000000000000000000000000000000000e+33)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.4074634262098477202456261501600000000000000000000000000000000000000000000000000000e+31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9362537824702021303895557050000000000000000000000000000000000000000000000000000000e+29)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.7695574975175958167624223800000000000000000000000000000000000000000000000000000000e+27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.5430949131153796097540000000000000000000000000000000000000000000000000000000000000e+25)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.7427444047045863749135000000000000000000000000000000000000000000000000000000000000e+23)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.9163115009072256171250000000000000000000000000000000000000000000000000000000000000e+21)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.9274383168492884295000000000000000000000000000000000000000000000000000000000000000e+19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.0731790610548750000000000000000000000000000000000000000000000000000000000000000000e+17)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9491312919646000000000000000000000000000000000000000000000000000000000000000000000e+15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1366198225750000000000000000000000000000000000000000000000000000000000000000000000e+13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.3570498490000000000000000000000000000000000000000000000000000000000000000000000000e+10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1862250000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.9135000000000000000000000000000000000000000000000000000000000000000000000000000000e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2750000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
       };
       return boost::math::tools::evaluate_rational(num, denom, z);
    }
@@ -2679,55 +2722,63 @@ struct lanczos49MP_2 : public std::integral_constant<int, 267>
    template<class T>
    static T lanczos_sum_near_1(const T& dz)
    {
-      static const T d[48] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.36662594316736437928923771651218082870790219434510733129873815200968646566980996339e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.76780165965526893166944674250172218113345269194305352999222919039854748751783233101e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.07970572889193090835848021094044050788957851893559287421136980839960026782217427894e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.14103116540076985021820709941614153683990156820041738016476143763552291310864305462e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.11895235901890827822967425840835669339942717903640916537446753898873381005535850448e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.26548471357135814759065586133601745345092666805731605105989839308832305900191949768e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.56856136042152636864745499626803467747701570337645969278665918810296351408741364840e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.48255074360054688238131834296168065172557135920905358164352154448630969015187687499e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.56619966800988637898793129440851486107980873809024863561425305126874295268067178801e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.81597333294282872581583559942700103331926900424172914177106074836091709159865752408e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.63678053487724707751260697626783885891593791493016491379265204946777211045670615960e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.51398164257933964710898171665986511410737733219980979417140085562924634596875563017e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.24278345602386851676210506047826420822246500559376040889647916551285989221630819711e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.88891626830459350723218099328412217578914954601038686119863249895652809029737934745e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.59719898181036663575857261276179540194083274881058286618169370083758218641306764946e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.64811367543293387988966817387441229757530457146808054159891759802567729960811992548e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.04201418909362106976467138015064536194810537117201428954061434907295912679183849448e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.13288541649508118041751198270788445621639048290878149127604057823054487014510567347e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.73151244996618239257199112314250678525910059470480205369884034575880974697338791461e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.13522814977566175652818016173551223075398445721839956765100980594656777696996995600e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.09751773607848160413869110673825438505378131216432708718954295924780177394997267064e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.61580494932170317026139049544442892885812277792439584113117496484172419053879898708e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.57433012294978946531397728731840486773642836205104228434646630602626154207102575497e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.26115172606869205202745132493304748075964471479903642930011237303391162925986198072e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.38298958800694421458738651547755286166537642575090914169204625632511624488640442440e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.15434025288605144031976010596974001946974995609543721535748916319261879201397044643e-09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.82356872364336815146383574702913568837734092081047520230601339834144374864204220536e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.65347968332361614985780283973809979932690029695650403412722596287871272868944164634e-13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.61330972151984338818972320382872350752985962075827056997941920528654516802241093365e-15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -7.65712722253446172294321996643259661334528734360491402384245881720504947974618941889e-18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.00315206806375905680927042642419402837617729582878141293654269070861386455343121457e-20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.67823488694203852929295147942658910943366513902587599688834805295280061153989766567e-24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.42784331030702330814913209805860341549196535898588904124741295988710093967131088558e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -8.48033607088050589024790469649076336393214555653483679072498587123824764496639393119e-33)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.38678975538457226036965671734240034395107611196492658679331149986658879027568426753e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.16374538409167657752796610509153125477921149181502343813699059314745306802450755203e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.81171114010755337144545373726087472870924044681995068325590922531565077520176259988e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.12518224599976943855815669111195755470966740275125423482269033756614972278324281875e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.34263635935093852590059444867684742593087836231966301216975070578889017560759389549e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.99309631968130547786945826997659785416033441104613988483204974783621090009511212354e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.97679666641473578922997037967978768575315112030381704618978104186395317308038799663e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.02914662367729885237175382124322264439002075945431846631322577735558916377073070681e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.86340999808161554465998036301386594999661959859518584115844390884231065866412899967e-46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.29984672974930250076096802152581521034785267762668779142172198560320648227598177519e-47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.06114476593975974108382448813738674408492134446936551295509200129676957425762855493e-47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.29100594893020385764408454293732511414412187214201378654051353911377525656418964207e-48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.01295708418471529474900073238291374279037984260859165547005675299775146592711994348e-49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.85645797686287223531258890899878578933576632756354490084215435591125736026369211048e-51))
+      static const T d[56] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4249481633301349696310814410227012806541100102720500928500445853537331413655453290e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.9263209672927829270913652941762375058727326960303110137656951784697992824730035351e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2326134462101140657073655882621393643823409472993225649429843685598155061860815843e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.9662801801612054404095225935108977904002486830482176026791636595192650184999106786e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4138906470545941456294493142170199869989528110729651897652377168498087934667952997e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.0258375230969759913527502498295624381557778356817817750999982139142785355759733840e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.0558030423043855628646211274492485894483342086566824594162146024985516781169314244e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.7626679132766782666656123523498939281680490327213627146988312255304416262392894908e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.3671346711777066286093979449135095463576878628561846047759456811238250487006378990e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.6153175690992245402186127652781399642963298842199508872954793356226534605339323333e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.9373755602608411416894250529851681229919578866115774473369305562033628341735461195e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.0800169087178819510009898255169517991710412699732186488007608833012065028092686003e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.6113163429881357240014185384821233436360839107514932109343845514870210427965645190e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -7.0800055208994526950912019754052939899262033086446277779400918426435279835354194130e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.6124888869258097801249338962341633267998552553797818622228028001697157538310910762e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -8.0821345203062947277822243784585588745042841720677807798397954250617939305106506107e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0897234684613304316686535121178451999373954297009955842614973223259353042645941321e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.4950083481830885847356672064097545823284701899839135264776743195466249025042048810e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.9937323326320843218449977911798288651196634496462091472078054583251005505547883394e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.1659790383945267871585567047493689107693027444469426401770619301894048344984407423e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.3811750187329199929662456874823737031712476205965338135458988288637511665389967467e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.3126057597099554726738230571307233576246752870932752732642137542414937991213738675e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.8603278118738070120786476302797971799214428999935477462676132231556636610008100990e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -5.7497497499750147559650543128496209797619661773802614023013669364107360500260024694e-05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.5455669051693660429433444114100199274899990967149528799831986363426701813268631682e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -8.3264707731119706730021053355613906861401420453549875829176477978488700910763350933e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.9452716333766656109625805591981088427443890665155986807469770654997947109460588842e-09)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.1107270143427404085533822649150071785436589803547989849458232547054059840123879700e-11)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2247407103283988605835624937345007318815870047594787786390767998944461846883100894e-13)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.0188429331847134597398824340892444962476368435762668313929678602451262836436731615e-15)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.9431143198672109701045920614322844783143358661530851155605617982604226639477903946e-18)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.1511473493622067561750500375000264321547190996454590396416983138367840485620637483e-20)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.6282967029324804059233959451615215356643254329321661581764544172041721688288262211e-24)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.5217584051959451141711566663295724419583710296958056943098481375601920843969902641e-27)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.7686779496951341450129898316334506462294006086177935245787611395642697303462481134e-32)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.8183279898437068462121010262051285364082674967144808177521395570040237794774928143e-37)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.2301356317533360807190133199588525842189842444453020346114472115201441728418314131e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0538087755476779873724252308339637373681982420524344896439951953765025296864700289e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.7368861518094102628071448870890238982875711317443189777819779346097156832497387210e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.2127031296187719256650789211253726767816659542004125362087789737915250037588745613e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.2845218026163010098046208410081722573197086178079121337275774350592686815176989662e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9013371187879239559027439498823204927228357549709009148789220121477613502450061401e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.2089862298013055403993867290116144511841012233395353799752061257869549127164945780e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4527554216741432380141011585082087141319941270266854468232919279949735902352803053e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -8.2837166837027744593760237442711271028335526295415770894642075176684832265233618094e-47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.1059350216220761035803511769514044782618497241929104348673618588819476720900045601e-47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.7687314351211090978609979306272584841117647148823431923713385159635722296908466519e-47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.5969462796000208210556070606779102539560199436191964981433237450523523642860510077e-48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.1139078862715122066066654151520960142401928001906787354175105139384536625985592872e-48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.7479750622279993094858160487261517850737208803407757126835554161719741165140561935e-49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.3023257271883644155548861805986381464362072120660374852325331311980696768011868477e-49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.3944877765920457854470382189260552086188360983214813092431218719428924850775816044e-50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.4340311277195491754628728769381617236158442845382974748650525927232846582643581377e-51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.6046447704173152191387256911138439680611975514728905319266554977285611063458373730e-52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.4634008445755689570224291035627638546740260971523702032261365019321949141711275488e-53)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.2246731300220072906782081133065950352668949898418513030190006777980796985877588993e-55))
       };
       T result = 0;
       for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
@@ -2740,55 +2791,63 @@ struct lanczos49MP_2 : public std::integral_constant<int, 267>
    template<class T>
    static T lanczos_sum_near_2(const T& dz)
    {
-      static const T d[48] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.96888487550957841138585220622994611985377489508130630837700057227501332853802783571e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.54685487861380185221232939396911532213815096219473151461939579496835151047360732452e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.55552167748949946948357664110976074745481263569802725437644778906661083814390424521e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -5.96594384244972046908436642965430637119152525028640569187886872989713864303356592740e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.61206392071125071279258677015155474032235397552388756144191669459747349464120963595e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.26386207619544812116284495283640666091191851380376198408981809802540783149068179434e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.14119209063000811010153319909166529923295169312754965782286511885151365058895055453e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.45796781987366173516756643389460485986669456101668857494954730722833100110613651939e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.57848002216691432249235663216198359909768823927158528746723212875688277777327166892e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -5.49763614406879724077940366200859712110749040051198851331880172109188055935892153627e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.79878440118422879619706786668472072947762184485364412917440713970863702012601831523e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.18117881690802831493078756446312359535362496025568649851035022806893921424585651770e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.04346085879989815616410913816129789693536068884338152664460700712557690664496356491e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.16203393160809415901576300558568214071599197484753461939177893151363492512491744816e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.38265924315387281787206504282410481919445750548305464376847792250029309946303762942e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.81511194797468462062874900113250266465621301462447801385359808929965375229616323251e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.70467183357417683453667167003713608362889484387619452881332522389524770233094455619e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.63213714284756057716179081387804854162483375452448157161319547511874432644723929936e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.49457336262308128548970424731422625668341066112088155314174120975542287189333019758e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.07620269531262256257667392994057559249714693275375776469485257399496930680150472549e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.02187366435225062095438319574039637826727962739349882824178780109324022923104253736e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.32787467733840531952793152972131223922164668925536951733638661285196165517774652382e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.37936454861394636073464067115999570083944553260438583828963060925061101644510914088e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.13900038094091115267314860504732881894801020942472019504308090210210731167345398552e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.99245982152457111301991970385956762536902876746714853773765158096202639164545608854e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.54442771789078363056076138819579948120113702520046296917694187019851573438477912893e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.94926914964866053119681538255564252500374927699409988373657464226793796472537754598e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.70422350226445404683228568613754929042955139666562491583132456753472072839819516057e-12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.76497022572067913016091674317545685518824311681605875941103548614928596445142654530e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.10315496743460248468022132288915711635897058766184880707096827157196752704473690191e-16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.44523155331686111418148572564943890979552960547133940740999458361025242160963413278e-19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.73988808644577660977639361852731370450420349068670037458430193432726909116710442573e-23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.81984174508721338476616177429473006273759399181666460057479840823572355207273441830e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.22175387586288279410299617080503779059482571464350109824108120007426231737351306256e-31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.76069628266069128881232691561697202264350068700303406802593331217743381427492776348e-38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.55797760012119196385166534789617212222293557097685410066659856245708610260816713241e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.05080524465178727911313037718933906722430509738224888801936471543177490693203242080e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.06172965819221083679631791380848228306721487317680820361950045678791125133333041491e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.93432331242636842233461846275246262853067820473357196595254072710231999304513059821e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.00748867278864769255014599872258605211683566333279390476878762044733272684660155341e-43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.28864237743622222407442194745385245322813091389014701339281732300960497092852607932e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.48268166001867959355256619834250603827306390609511540411093653502476081933431007754e-44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.12528729298048868682661828587192615782099352227112063181739468363374124346195882740e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -9.07612869947754202550701651568771230782100517153410159160000452433811651633069544830e-46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.52878107636588388950021856856509972417665723455977954669464087724444519346925778688e-46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.85993987583058920731606562273777225552135287406894580374509213860879421694626894310e-47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.45935754590553989061937536984206183886886144778541444482827659230313539351404405283e-48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -5.55596198187619704372842019685051223079581761704170979479661609332351755409245768399e-50)),
+      static const T d[56] = {
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1359871474796665853092357455924330354587340093067807143261699873815704783987359772e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.8875414095359657817766255009397774415784763914903057809977502598124862632510767554e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.8476787764422274017528261804071971508619123082396685980448133660376964287516316704e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -7.4444186171772165373465718949072340109367841198406244729719893501352272283072463708e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1194120093410237139270201027497804988299179344758829377397770385486861046469631203e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.5357088952571626888790834841289410266972526362527135768453266364708511931775492144e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.5786127498932741985489606333645851990301122033327283854824446437684628190530769575e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.0137191034145345260388746496030657014468720426439135322862142167063250610782207818e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1043282398857092560432546685968118908647431787644471096079379813564778477126420342e+06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -9.9163139177426012658354764048015319057833754923450432555380434933570665536720208880e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 7.4010907978229491816684804764341724977655263945662331641124141340242633003517508734e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.6169234084041844689042685434707229435012900685910183054712320472809843835362299874e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.4153517213588660353769404140539796364318846647922938442928982516763682295297524025e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.0612877847699383856310204418767999963941175773527544927951233517414654065993562292e+05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.9161022337583429443319078749411063125143924304273472659235111671109967684138896371e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.2115062080034682817602956663792443265985654149672855657063890194977099012713284199e+04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.1324805949350810193947943179103430601921304099416931772402636138580376468344900971e+03)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -6.7379854977281995958474241831424455939028898406040636148869222006236410315246590813e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1982547830365481876880107367272973441376153376561639433022240961322166151300388030e+02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.7477942737376629095840094280792553329439356352076603742418189295402785845496828618e+01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.0703715155075453775002558378654461695986020593253642834916629665157095201951753511e+00)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.9675866846243159020907742164534290169104130230063615572789631974066350817947062221e-01)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.4780561158714357685758956261017689353220221023341472401836356861114284203430539079e-02)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -8.6188339219787319686113112867608363101891398970645607178011869309209804235190901119e-04)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.8157866597647120851117681906042345217930339391652255480834165995078338419417330285e-05)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.2481320382678181695580703583602390565135442535050898393382403247198998298046344360e-06)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.9159483230174733349570293758760922152980844047473628166544981799492351078480622954e-08)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.6629576379996951454117430064764364032095890196838102664116218770332578145496215211e-10)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.8338633562069325240602901391334379837235954960205324388722028354858275502279946625e-12)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.0262311774099493927119217222064229499121659914970978765047236920420564019570051218e-14)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.0407678912374899180410563256969325940215095079830235805022567411720384237429934979e-16)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.7255616775185743686583950617043659309702235282144322436444914063380593981448767314e-19)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.1434762424301802086970046614089097993428600914262940192954247147222512140342020251e-22)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.2811050104947718753668138286684667456060595320836882460657390484001848305710926658e-26)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.6472071585409775242391978767682093973522869636260937895265262698161653967448170294e-31)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.7256607055318261608651300407042778032797661723154154620044497458638616772687293939e-36)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2336914691939376212057695014798607076719945066572302277992040650923577371403732374e-43)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.0786447260639215447891518190226750925343851277049431943886851989702400712288529676e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.1025728477854679597292503557220243198932574654689944030312971203381791545284070615e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.8158191084622128024881877808372136805034582816867095109911304441480739442791111504e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -4.9234747877490011456140079812669308237793558885580849786063897631770733025035207671e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 4.3490836759659078559291835803157452697088321139262167213210146255834532556301891370e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.3112546247213856964589957649093570444521154190936715486464158458810486032666803106e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 2.1776700296770363161098741319363506481285657595677761712371712460328658791045355723e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.2417232307174566390298057341943116719841715593695502126267674406446096534743228763e-45)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 6.1547673524314003744185487198857922344498908431160001720400958944740800214791613435e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -2.6513158232596442320093540701345954468693696224501434722041096230050093398371645003e-46)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 9.8887754856348531434071033903412118519453856283236928328635658056271487149248163047e-47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.1687328649763305634603605974128554276109745864508580830005398092245895954643537734e-47)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 8.6161736776863672083691176367303804395378775987877354282547095064819083181262752062e-48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -1.9521769890951289875720183789100014523337064918766622763963203875214061068994800866e-48)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 3.5893201221052508883479696840784788679013550155716308694609078334579681197829045250e-49)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -5.1475882011819285876938214420399142925361432312238692258191602240316479716676925358e-50)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 5.4033368363711826759446617519812384260206693934532562051784267615057052651438166096e-51)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, -3.6926203201715401183464726950807528731521709827951454941037337126228208878967951308e-52)),
+         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 267, 1.2328726440751392123787631395330686880390176572387043105330275032212649717981066795e-53)),
       };
       T result = 0;
       T z = dz + 2;
@@ -2799,412 +2858,13 @@ struct lanczos49MP_2 : public std::integral_constant<int, 267>
       return result;
    }
 
-   static double g() { return 3.71521093750000019895196601282805204391479492187500000000000000000000000000000000000e+01; }
+   static double g() { return 4.9921416015624998863131622783839702606201171875000000000000000000000000000000000000e+01; }
 };
-//
-// Lanczos Coefficients for N=58 G=4.7377167968750001136868377216160297393798828125000000000000000000000000000000000000000000000000000000000e+01
-// Max experimental error (with 100-digit precision arithmetic) 89eps
-// Generated with compiler: Microsoft Visual C++ version 14.2 on Win32 at Oct 14 2019
-// Type precision was 334 bits or 103 max_digits10
-//
-struct lanczos58MP : public std::integral_constant<int, 334>
+
+inline double lanczos_g_near_1_and_2(const lanczos52MP&)
 {
-   template <class T>
-   static T lanczos_sum(const T& z)
-   {
-      static const T num[58] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1113345018281139401900617648632565892997531886271137869532357720305909403460902551816191757935253298297e+96)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3306998523015859302296206498309765162943025964850544682652937543993544826195909937055933931442768067675e+96)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.8268352474100341852641008414682924186512501342670048541149232501353823124314085480609221821688640650080e+95)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.0141386651493209831831274089811845202892902987250465018037980182315440505121630111661568734223655786214e+95)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.5471258592914542867143021588167696855338160407933457150021303941501653183920330822783098409082225352649e+94)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9029900619671536896112969373037726527696919271039767737722503312395772965346303367519600397313792277727e+94)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.4640693221647807642599419508017238730661097576373283904791677661939143319337033201070793440010339999715e+93)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.3008318491825889746629471128738097186407559167000216981000503166575445677111681454415332001004453692360e+92)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.9581961997681479620796339921050983411541681934353890086635121221338490738854914613804353855734829750740e+91)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.9562812093757389383361734216065083810639336069848105427428961256383580773444097085298844542948261561976e+90)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.0204448099875032766488461246324914875195022845573308192494619777200657405252573402181380342443147295173e+89)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.1967742477741068422882850261828584111953166907106815923693978537447964053382494347755201222673169434806e+88)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.7934308426826323386245296144249798411531042807557571947289014719343462128587532573403065724298496762577e+87)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.2112731316363645590406244691358512085700135781552933145962419229534561671703452680159817420544888863655e+86)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.7792875367286636291574914918267428357586601357931867786906344130539973047706286380462771311772443260655e+85)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6729889167781214645382609228554520670924462597343847547527634847733870633193570419233293354907537898968e+84)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.2212896890317209445182351532165347688163702283356828888187120214401748895306876396481747000574259149233e+82)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.6696330100177872775181285832060367195698947756070274789550514016487770556676430692662838020948055174819e+81)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1787790436987713717592679695802576546659292017904142826938775295267502136179724011234775858106585474335e+80)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.3897471960941486230091766140467565375262975446763006777927562006563131703283610364746875620601313483057e+78)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.7456216276193058883301725852613487104982510349671722342387971953607146505494372335184541893296983766398e+77)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3855091017101453942895165907767739025127711826384743418432444735139729009897407793448891996393706658957e+76)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.7596919543541505311176214833582242571197674817260097288825507658966682365463135538963387631678553863542e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5205308568827525377048378465545277453459194177597465928758908233213456983481011601239823019085100837607e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.5219482007379940303673464060102227421305538751659464891709211634879751289944728765835405235116911964067e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2529929196659743450833612479027982672526994601606551595908472901860777472333846227605233498599036089780e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.2371343799933848311703711400651007221131224388690941908721236718964833912418768528725638940635396117593e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.8015422120873735048084230762717970714811562909437854684093754471976926045882197320273930142628411250042e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.7544934847649309554128203553793825206530899558440305080175611169946112759760674627144360103537889679591e+65)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.6825279122107455550724823529764700516671135432239079326787536307050166777000218851702259835300111357922e+63)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.2137862491643897667607321980849893924427698956617156800113142641018717095876369593791167006646811605785e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3186571319674830310069793304531422675865920550412368667057521060523822178148626902742473745717612071248e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.2485774541577495056605563690047646700517885331946681444187667959802672435192052254156475697343336771638e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.5749708448011926909660539105173117507305781970952738170400845272354829441805660173686553510885012106315e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.2957728089076810011933348982855845071484336995217889625353037764527196874992238794680831083872659220534e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.3029702073166140154775964636478493296495204191370975362621002042260278819606865308080233433968063616502e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.3651754658248543289835755041517884667332033286508690963566578707866450840862377843752246373050313956333e+50)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1153610110919853077136756888034644015689784357746290647672760493336488593590043112457135368750990637667e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2317697361001624160827173449861094521356739436250957059660912760537330301205792128544135654641326400704e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2591336713897064687825047779362333153357928528455245343833435858589598201567338554890557167949204480368e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1888395650074118534283640535831622534704266864697448915278695723452804398372734472806777342045155424277e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0342195380047963732482565081644533382537722066923561121178973781344452277931733870503748282543943428982e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.2659603644818244197377849119572544438113712679642935412688508428331533577481416745415954979034017913781e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.0493876469565505074955014266411916314577665137838261525037575218110760155069631757821913430706010515995e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.0380102035661800729809170954585443393379101722448652003355183633039922242269533846456702077836461601594e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4471701800736812643301636372332435764064729819100848382778186520311589961354650397132342954205946278402e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3391793076015860668513073429148720023215553662036803736563341850799950224212365984411047979319730267348e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.5746079755559823667940853958792940224952894096446926758424644873786146686411034227207764327098030858365e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8730952802737845263408235958198085714879899902329571556827316641606659145317043632556281422581317630775e+25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1068860106460271425431255001071933519142520498723285368106201466148952145283909421951418316204387374823e+23)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.7146191714834483705600971071352976348572227109511068140706241351872914486137201205172098597005503434574e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0693465808661148698636384310734985694414606785941298207428612238748657882890467389962396214120403612061e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.5877812671795420049920049903121324610843253367633375770943367999226546473657225178995404939996916553769e+15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.1199728232559097639450648660234135896472362777482676055586950665599850474720777665093211412423570836354e+12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.9536149625531631518225658997937689548178270704423376010017262234330926444650292977902802706698285898435e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.0978434212942028068922584596812569730178537381770594492536210144311893565241511848298648224631091914130e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.8136582389003336880560289199735195790527296500214034301547642961678068653936021531092803113827675512051e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.5066282746310005024157652848110452530069867406099383166299235763422936546078420094024669537723756981791e+00))
-      };
-      static const T denom[58] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.1099858780486345185404564746372494973649797888116845868744704000000000000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.2787481989562818154790285585287083447455750564964755439725051904000000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.9814423801545723353305894697802330693700024131737540066597268357120000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.2379872707088650213961476468088967648845485386801302969710798700544000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.6028610849707118786878466090726746922395786229117545420266938564608000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.0438085338641386367983933867412545578566598680906745465073101805977600000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.3492380371843850750819852073737242436575952022390816483000346566721536000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5102990983560640009327873678307954320470630605324516076646299828695859200000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.6706536806860658574451791386582141941677796433514743219241257405513728000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8043159910377823217375261881225863717725312218178043012454139087028224000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.9335160303959039103395501372789994167981664930485977399292586960638443520000000000000000000000000000000e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1723691196565373582067598608574778201485664959896330847068435199126667264000000000000000000000000000000e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4438352206893499975371296011596621640882812103203541286914698812249866240000000000000000000000000000000e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.5035118941062978428961903224471555396129604077556196563177106772688896000000000000000000000000000000000e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.3850308579063636618912025850466431356280013115826126911230283854233600000000000000000000000000000000000e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0836900819838640440767313247219165663768918429617679815795491004563456000000000000000000000000000000000e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.4298706038662999363673291534756645260294395901949985216872998030991360000000000000000000000000000000000e+69)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.7034492632938290783198763770876160868300549275946097010473332643840000000000000000000000000000000000000e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8389252775111283069889631347879462661235829004870041197088140774400000000000000000000000000000000000000e+67)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8045026245181087909282578887424942187415211828585867350357833779200000000000000000000000000000000000000e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6139415015963261948795856116734033680672939822172300204078108032000000000000000000000000000000000000000e+65)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3187949670862787149323475106066210874520928766305564723661651200000000000000000000000000000000000000000e+64)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.8652947935638867544975258598123447770317269214048194873129760000000000000000000000000000000000000000000e+62)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.7677767608518504817918794029244339508807996285424723220104640000000000000000000000000000000000000000000e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.2641467556495415387682543812562093348191054073538914270730400000000000000000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4706517237142185424284275343767027578875512836847707758280000000000000000000000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3177422716201009039921461100044177449498643771855331909700000000000000000000000000000000000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.4750611894960504179018603471357527802382408288670161342000000000000000000000000000000000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9330478552107545132079399426533304480054308936780642545000000000000000000000000000000000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2252899213008209896248783169149861832238011945022246000000000000000000000000000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.7217402128877734970019794026056267173695376012268710000000000000000000000000000000000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6785124525594845202965146591601984920001061237741320000000000000000000000000000000000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.5034829951836538559219701088754272365603191632587000000000000000000000000000000000000000000000000000000e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6637415534451225329152181513653760874075278100800000000000000000000000000000000000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.6347190324222080575971451540788329488139570600000000000000000000000000000000000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1887997793364622891010571019581486512880887480000000000000000000000000000000000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8047716936655096027980248782543659943937913000000000000000000000000000000000000000000000000000000000000e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.0790225058170194637643585929666817947860000000000000000000000000000000000000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2084757755139694726502828251712490452850000000000000000000000000000000000000000000000000000000000000000e+40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1993406165887949960123200495814460898000000000000000000000000000000000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.6561413270081694853593737727970949550000000000000000000000000000000000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.5369993949587931998758036774526800000000000000000000000000000000000000000000000000000000000000000000000e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.6151991880839964140266135934090000000000000000000000000000000000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.4760566491969897737280290058600000000000000000000000000000000000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0621766041618690022809397383500000000000000000000000000000000000000000000000000000000000000000000000000e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0668475851162648374876202000000000000000000000000000000000000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.5410679744103301927030500000000000000000000000000000000000000000000000000000000000000000000000000000000e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.5395191798636166637180000000000000000000000000000000000000000000000000000000000000000000000000000000000e+22)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.2147541393617700530500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.1197409850631024000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5899910954161520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.7660425636804000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.3384219373900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.3043596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2435500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
-      };
-      return boost::math::tools::evaluate_rational(num, denom, z);
-   }
-
-   template <class T>
-   static T lanczos_sum_expG_scaled(const T& z)
-   {
-      static const T num[58] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9525834451195623352844833708766019251484824420589901934439764663785971607902920873854007890984226025387e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.5353913226536305547742063023255223178577430351061832712694094731916543407128432857596013878418835545541e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.0794265040063864629969189140227704423008747481150565046014672784314863153912417986968014303182196879938e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.0079363228400099355108372825384509227179448653556047031855632715439781114354847693263728085548142549876e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.2707926617939589278984760255796767920967443801395440059906534121478842405887081438764736244178311493742e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.0558467715603214792617326562510713807234351435955730720590956416562782623810902927804516780978093617536e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.2033080198136382677487341183423922900647133007317553822084317473855699622210307747112227636535549617309e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.4083202075984620999390260696805188384092629914880295342492703293697714617999890327029040466923272486691e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8486472680848031160157166025706272700120860759432294711200940780548927766558565495831077710008357816723e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1138175900123376987163744326763008390621758864911227853169463977789770550938948181501331329408292888705e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1308645173446504769606114641352353002279158988307024846586220931944095152963117782251173128553590002677e+69)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9120324679281068850671805700697238886511656051607969710283305054986370771314011765262161774820057407221e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5391934623114467787956807868296099285488891013887607698670475417480968323895750297127042280725645864237e+67)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1188472337439846560727348944974065682611782369759313015986429928637543111162293072546541343053710871237e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.3839859706266764054133980098731552638450995195061568584278432933554090666516712057667084959928750476621e+64)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.4447818108967399523602631725512074937872788923328188245441957349314890139383300142665492699548078016636e+63)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4499038978543131336483547267337201487870950383856380855972848092343622627255235050078874464565496828787e+62)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2406238713440761680092008034709525627435037404776653076097934320335762078719054009676170121443275896208e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.7885604418978046593206212118683810887087891637289025925672325034976573417819599577035132403057170493687e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4946595358499347633866345682061171079599164941304972231143049023731630101503606670560705515260702923050e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.9513336364509343072555606544850997149882112871146960235297930573184577313990835201997736426755771031690e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.6810080403717774179828377811768440096006474456859136430725963485797286723671499145937476199781240726843e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2645506501577530162354586527854723438171436013868785795302304165655061134281691393986730787208175906833e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.0397326173536285938710693563469993609385607650335155744195392582126325319144559249104863671555936627244e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2013871048927633852181093624593869925193443374649283179426834256685646298857112848793626713837584764108e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.3289402473981501234144402953028274630427307351359919167469712295902671507115725494100349633541940933204e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.6003893195733192859177412982185685700998370832033861854329854490539688708839874262744736474012759445436e+47)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.0727066732760648460132569879963196679351152547539542083857690449447906448979182035004975167951264229374e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.6613224093786683644702502032231164856098499632779487718555251290733786904948988026020403761370171127380e+44)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.7837068244515233545220503730640329863081890096623187288769939552653286719974960799952261791747246686408e+42)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9165522010589216370481372290739111949387650621903781998282461665273890471374114621564713215060999778073e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.5033963322756782307786713227898388231893223357237704976668993902202940789294809098147971301691772648755e+39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.9740002270190565366640741207315377496247453294707036602010614289735470303392852115947439612907179897898e+37)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.4979501813196320177935632677278886186231320810970746337833403723731191512041559167496248429116298871699e+35)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.4069761263574572480694806529063097871169957005541147202721661005052475351188525148368053997631136759790e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9402465143351975112300028774197323450509816779255592414045815705522691518043705429706146342655130265366e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4881313407932962145111410344090747527354995727266179099775181263231061106933689865989301929428200117871e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9632810384855297696182113289305607179489664745076688933167066674562917487536504070129264115660678482556e+28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.2725546854039254943463934183457508258081242388204842730157719983831445104894295952204798603845536120509e+26)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.3452549409942328202733488146109233160716224388189413469297783823577482916724384652184656289642575364301e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.1584981954307469031764309294640361429335538748027906889408285804565757617154922327898215115914925102238e+22)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.7477051072463293412749200465569024873771231987242784210248733085001441979676968452992807610739566040156e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1960928676322401992340089643560231337218499440045721085448636142070840811937842162960498037401931828261e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6071958343894951054088987834710923196788323800906338042869660264064639861175574231931711270452905023878e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0728148958446892912836806181637101367297983133466225777574815613761623459000110314136961372678097371209e+14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.5016195836538037540865015222440859129132562974585463183411281203357391116994585543064375504964287033151e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.5579194627421707093560391662678700402228252243270030776955569538161088100804816540797427121002521848777e+09)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.7467358958842104945974935265631802960291549549388120971605962335321138414180962067591937089645593587253e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.6332135345687020156244092536439323519014928693505240553789259043703120308196994214855462894182573058664e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9407647340128848401194943791119430377408353392667765444895085026094746239619902099149777694224783951328e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.8689665916105177080976558363071196803124010350312199134246436579120098844674440713135687985135098450472e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8410303167649082918635413442316246381709300383012975083202578569099476956148029095902566747899894260699e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.8751938471236167190844006303614257144787097468775849169694452270347666880072332030058767126104666814717e-06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3602697452963248452045411104106027969968697679097453973063118187262717386356657326020477164267694748313e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1131092239698914177951080885440635365109643513308304020521218234027520232780450142616357759194523396831e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4171068051802330111071549877540818528598812224565937952488425520621143590937182779724061728889603469712e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8102465534711886967772860840717324393645550944967932350301450628070653877586909697550907928519183677886e-17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.6595873110837641575235810188999693348770063449340247652053167124146826554900758076335155425689417108046e-21))
-      };
-      static const T denom[58] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.1099858780486345185404564746372494973649797888116845868744704000000000000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.2787481989562818154790285585287083447455750564964755439725051904000000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.9814423801545723353305894697802330693700024131737540066597268357120000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.2379872707088650213961476468088967648845485386801302969710798700544000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.6028610849707118786878466090726746922395786229117545420266938564608000000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.0438085338641386367983933867412545578566598680906745465073101805977600000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.3492380371843850750819852073737242436575952022390816483000346566721536000000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5102990983560640009327873678307954320470630605324516076646299828695859200000000000000000000000000000000e+75)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.6706536806860658574451791386582141941677796433514743219241257405513728000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8043159910377823217375261881225863717725312218178043012454139087028224000000000000000000000000000000000e+74)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.9335160303959039103395501372789994167981664930485977399292586960638443520000000000000000000000000000000e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1723691196565373582067598608574778201485664959896330847068435199126667264000000000000000000000000000000e+73)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4438352206893499975371296011596621640882812103203541286914698812249866240000000000000000000000000000000e+72)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.5035118941062978428961903224471555396129604077556196563177106772688896000000000000000000000000000000000e+71)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.3850308579063636618912025850466431356280013115826126911230283854233600000000000000000000000000000000000e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0836900819838640440767313247219165663768918429617679815795491004563456000000000000000000000000000000000e+70)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.4298706038662999363673291534756645260294395901949985216872998030991360000000000000000000000000000000000e+69)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.7034492632938290783198763770876160868300549275946097010473332643840000000000000000000000000000000000000e+68)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8389252775111283069889631347879462661235829004870041197088140774400000000000000000000000000000000000000e+67)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8045026245181087909282578887424942187415211828585867350357833779200000000000000000000000000000000000000e+66)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6139415015963261948795856116734033680672939822172300204078108032000000000000000000000000000000000000000e+65)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3187949670862787149323475106066210874520928766305564723661651200000000000000000000000000000000000000000e+64)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.8652947935638867544975258598123447770317269214048194873129760000000000000000000000000000000000000000000e+62)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.7677767608518504817918794029244339508807996285424723220104640000000000000000000000000000000000000000000e+61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.2641467556495415387682543812562093348191054073538914270730400000000000000000000000000000000000000000000e+60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4706517237142185424284275343767027578875512836847707758280000000000000000000000000000000000000000000000e+59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3177422716201009039921461100044177449498643771855331909700000000000000000000000000000000000000000000000e+58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.4750611894960504179018603471357527802382408288670161342000000000000000000000000000000000000000000000000e+56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9330478552107545132079399426533304480054308936780642545000000000000000000000000000000000000000000000000e+55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2252899213008209896248783169149861832238011945022246000000000000000000000000000000000000000000000000000e+54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.7217402128877734970019794026056267173695376012268710000000000000000000000000000000000000000000000000000e+52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6785124525594845202965146591601984920001061237741320000000000000000000000000000000000000000000000000000e+51)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.5034829951836538559219701088754272365603191632587000000000000000000000000000000000000000000000000000000e+49)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6637415534451225329152181513653760874075278100800000000000000000000000000000000000000000000000000000000e+48)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.6347190324222080575971451540788329488139570600000000000000000000000000000000000000000000000000000000000e+46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1887997793364622891010571019581486512880887480000000000000000000000000000000000000000000000000000000000e+45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8047716936655096027980248782543659943937913000000000000000000000000000000000000000000000000000000000000e+43)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.0790225058170194637643585929666817947860000000000000000000000000000000000000000000000000000000000000000e+41)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2084757755139694726502828251712490452850000000000000000000000000000000000000000000000000000000000000000e+40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.1993406165887949960123200495814460898000000000000000000000000000000000000000000000000000000000000000000e+38)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.6561413270081694853593737727970949550000000000000000000000000000000000000000000000000000000000000000000e+36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.5369993949587931998758036774526800000000000000000000000000000000000000000000000000000000000000000000000e+34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.6151991880839964140266135934090000000000000000000000000000000000000000000000000000000000000000000000000e+32)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.4760566491969897737280290058600000000000000000000000000000000000000000000000000000000000000000000000000e+30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0621766041618690022809397383500000000000000000000000000000000000000000000000000000000000000000000000000e+29)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0668475851162648374876202000000000000000000000000000000000000000000000000000000000000000000000000000000e+27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.5410679744103301927030500000000000000000000000000000000000000000000000000000000000000000000000000000000e+24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.5395191798636166637180000000000000000000000000000000000000000000000000000000000000000000000000000000000e+22)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.2147541393617700530500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+20)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.1197409850631024000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5899910954161520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.7660425636804000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.3384219373900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.3043596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2435500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00))
-      };
-      return boost::math::tools::evaluate_rational(num, denom, z);
-   }
-
-
-   template<class T>
-   static T lanczos_sum_near_1(const T& dz)
-   {
-      static const T d[57] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.7428115435862376558997260696640294500966442454383057764865555979364261022425976429085092772284462056620e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.9098470636910381824837046571049540905024165376037355421260734899535717859205986796003654941175663049821e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.3238837075893790405047962895917439384623673303456004530561387555917370190498457070337183015927777421697e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.1818710867341557832686340441113771687173935259473061186027784614571488561024113573068868892276452685792e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.2993023860235266500362186023069966658235478225844203105044378872946562122380318851444839578192967323002e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.1912180368478885109223112981184136172284705131966546680563227042436992258659147484337283480302880786198e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.6139396362168514560020167846095021752825297585055554665973631410697906644150591916500251626224775776603e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.6634802529570780684302635411632208905442609915247254971321402103134398787017804507333676554065934886041e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.8912442659385178766302183254171219505160153159736231877672680444314286802452078408167890642564966971613e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -8.5495375341789279888846473669676987489917192922529063440714880612919546655027506056499234132070763181503e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.9953131705119738082952990229447045802828349018683164227185193391425402046621590400831377644280156201943e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -8.0869264878440576629536295016426099545140305890893332059172420721937348112425650207439043097833689822279e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.2468943229845282686806294869840458047361754209121185638286960316366706592206130567941492816463381946909e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.1630054452110204332042164710368677551444071577885528134258060122924060097997330723219233292551334541916e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.3999790605522096466954112874401964638803242076322683502391870253501264993933977365040197484368089793844e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.1989159366950562464845132094716096217280130489202748985857413544679377185401912495211215199827572320658e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.1934569461829331860249338515130842345952840084924773082558044904616988546739452572774668343010410556738e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.9504509773595632752455387440694137287105978110568834596383152715430739170438241704706104769027458757024e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.3443645806133388465801728173699557032879027729815842645734341879259895367471331502957361274245333765268e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.7841389657268783911632604958857419096159175608100099391870386517930613345705029477317961997797817456392e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.3263071690820256271926147120746615152585668319664536987434389730938667811945831461118672855948398156120e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -9.0147093132626919930705734140711481562906727339902047165060887486522943229634999363817715017657681660287e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6071102334369619355078667017356321869894503980205853863658685021270881486705453945159213607404060788769e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.4383630842681764529222336922814378927628353308340684972787496418846394508904604721467821529575751627808e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.1286133930578257063116405165630725640730704580877093703762851704304775232899279568326548372516108061737e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.3692644530387989631839105618463769604011314569959807313957135524319268073994325844277072212634894718838e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.0185001434002208420172349105229077528666279911019323889220715333407026262532945659702898548882557288755e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.2263062380436433070464690537097677591705999260831413712451347815254366329816629201276858957857633159301e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3353139137616007516399230327860238131259262384241927446052286747295202825849286263834250215682608257253e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -6.4195296490132509971486202730620553572364290374630355485943647261186824263045109480840776574102283117802e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4317122347228636250935502644177076353230092364254437169086888072416523402594888598203831115818706298660e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -7.1116401895712757982110113602984617019673481361481571387831251493876840058692034827601429496435585930404e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.5670513725610592064219547014678059161831695745208975662601768645833855387548399162792665797683105415471e-11)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.5260646573782426214538742421235036428884108667170155792319000553615370065204316405736286181192562052741e-13)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8733941140402994491303889414468143535352703737984260742434438594748723811519620261843045417069155536008e-15)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.2056577386533803436177435861654503857156683256162837031477537088773467287029340043192251326622052870465e-17)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0800931908111468667692114269177968638854301916581458483888602672737990097921789711610932672475861001994e-19)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.1394496063229749361320583264730160299755358905685423988290847461006304721866926670065937080941317261860e-22)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.9274792450690899704710418936228583371317511924974285800543619049655797337986789330520046119470213637029e-25)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.6755223694460581147198804301148887855673388834174147952660909117310772380696272509534022412162907695615e-28)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.0900225572290190698649005514102451202434886376168031607266730359956445823401555519988657304185446296554e-31)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -9.9024654365441546862123770751558932020185466144030552444525982172062830502919077739315180881006251414076e-36)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.8401409342622593684683418781548298452423138616374012775158698166549875044639516398318322746270349752685e-40)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.5509630598854356990909041057867643490325454268799807828321700754551551638916414252086883229952366535870e-46)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9657368621557895021941755410664403576678059155205990324521617023894341207730153756506985102036313160050e-53)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.1241524357510805548447946933511907560696760445486904751298400852883111381333879290886698299626153350908e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.7964162808880362344077245029516705444495147547810713281233063336303852616170950226238109362470235010501e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4347533225708328774658804669618167169988215409141087123873615495103598105335608364600471221104934664685e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.0479456512751620605515259329413452300868549663188231386090986433707412031359388913176316853836715844262e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.7702413521297716432095744498633554542922110264197418721766960511801656053258128107225421844535437414965e-57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.1172472608352701420007786830697096251191397605488453881854169564652213625087310098345004527869954910248e-57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.6812745632569367999094411216914045337299158629329933113885292569194336792226670477775358040058394820261e-58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -5.0940899331938988550733986571553993560122282178667089274000678435292023664866549561623149093538369388095e-59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.3990413208296530427672464741601390159299766279095164840741566288983363882627013060272921361169788365065e-60)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -7.7457129143553309783200493485805274806723421714099516756842649457968744562118823820376006640033350414786e-61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.2197041624023821332095587670691140585500743194040476924703015039327636848179534186153838408314119752602e-62)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.7047723462914761686649775942852334082321432815609988664912617018852671864913042227323649381537503179251e-63))
-      };
-      T result = 0;
-      for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
-      {
-         result += (-d[k - 1] * dz) / (k * dz + k * k);
-      }
-      return result;
-   }
-
-   template<class T>
-   static T lanczos_sum_near_2(const T& dz)
-   {
-      static const T d[57] = {
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.1662905928411697905258405605703584854097058546117590807018322943510409180314506715189727704455120038255e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -5.2865276330524469503633315971419666291446796012439883450060362841602955272110829770969508625348151344110e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.2219660233923727011658095806761811032946810239961697070082822527681712138952842835075740681056558805545e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.1471898769829091933140257345448028662421485176900416920959625594396387278224755880120811584841740984425e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.8108506629663017023576288202278104175560258464862168051112507988271579950339846330515110250714726935097e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.1641711509053717182383657533380473756042975817599106212749608660372803916254884680397716414106410031258e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.7489314096332467747675642425312337606864580547949737826112168114861342185432170188369658631861013639815e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -8.4724786849037234839356479194796060821229710729537665905710787287944594232273268923957076043820505152123e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.2519817172723530341690766298268651248835138906207131843033724432774951682486028564360090931772389689559e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.5532557359535150161664447223551521375257233550726531311510295929236015954526292484349276082718903034254e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.6342429895113330905046033016646335037353665731613082814708242545769972330151611687916571207590466290675e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.4692098728454232462170975109580416322729103219472916098312631671127459727620998375190829900768135597920e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1349180467693002337442162064332669746019375174297711955789632954762786417078957693464106665366428215075e+07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -7.5632302457640823075347957970491681679223652407676639065204661139779189254891918422939089928834865040327e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.3602139028787279699176338906645576475531513654199858202869033753097108161316098377414795783646795195944e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.1781564770643699404196555460989570673904909639666069579972319801392840126860473187109481731392038690946e+06)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.4353253130211266653540571778153094858600293629830279655688388322741879148986220244682882658942335696445e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.5435240282512309592551076592408102377879926851607713336111442642626445924365822019934119240733876795141e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.1526261667865026060062626782458367235346781022115660163078870751778821943822555542992468135865376114967e+05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.2413730814968410697200758155304075536237935327710818457186113369696959175294570307981528264101370866348e+04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 7.8599121870734324248863589686279377309239133065805881581800599402339736200679855503773749459170204132791e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.6377668257261558531404127005983837331367557885561101077531977908963614729639690754651655156526373276599e+03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.9197523005380738606902261922935494412976764483416941348495962454277708460181544072006267228271644673220e+02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.4299489087401028354837196175165054006400597113077360830473379437347868849689360216846724154620950362855e+01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.6839760968600182694175565648725095464923929298411152920412000388870216851203160830044900161240884736073e+00)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -6.1211841186792218837353890586540028399627732652134291573554656108241153104326807995702108419307165078338e-01)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.4839254672775355063516929562453773790762108550565402409275434242243168512055903461692839292134763272349e-02)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.0446900436498039824930882038167913752019117688189621941029942455212255095042589886820040572146790228293e-03)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.4259604540679199219674266589960434988970631237379997092121152488502215342212782655207033499356597207732e-04)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.1662819432736824144566608258931608012907080530838741239388324423687927670373421600053389501450361346193e-05)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.4178658338791266451928074758746505934456557516996342163398372684287698861436808924171077524254379083060e-07)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.2920226237184384323812413019935857990607979507557513737013812388314162555859654820969350110668735340875e-08)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 2.8469744980165771885329432448423013838689752067078815649758371478630140330027362965330275099502650356588e-10)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.5892826398814320794517525606378651211265264604594412375068674574147845337527175224917342725746156587979e-12)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 5.2203009477948187935105053137418678388241808213010074775815651125432941229706488789085110080538814893051e-14)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -4.0071764354709508994124453699849221531650525550222671429443364906737525324879927767883427021892836113984e-16)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9622826817063220108064709012206725989960307918188611950534485874633362779114658729325037773191270734438e-18)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -5.7036630218461017970632409261270377964650553992557669797810281540623485979537248227679839983488911988094e-21)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 8.9521045677595146905259180949264876791866636312953998390445326640202924376790113203607493358448772833037e-24)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -6.6775848168912941217401852995810450906306734023598389296925437100201008270660133423441040356945585338087e-27)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.9803220730550206978978787593484142931342246644534949059896766020244771367805337770466949634458076040872e-30)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.7990518408632014329157379404081596938445109431006332980973114098434711412087164821902160534448534060827e-34)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.3431158699278209062613044372715762567352361096055698830148755308547762997581572887297656338501121085689e-39)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -6.4512889953126515222750706142725047033542840408835574821053782432341231211557553861105639807627133237603e-45)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 3.5712949902991134825521996829159928713052863755852691744249239606303690103524531369836280748984998481830e-52)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.4759729775024569614177814940895080213705811461280570147704308137991423094447188671055911764625031287276e-54)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -8.7139930908855290554513295892599839263800779861752158476251019536427498588557825717368115652274945883813e-55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.4233907960475632932218656634142149345608818585031048657672084471779614927408553135306513446078671755098e-55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.9038779434600254520302015223066920881918842711110146920259738288262023701119647715089263879918197432213e-55)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 6.8496675787588211884718935004472008052724911912938728434253127344504858415646126692300012586778132949530e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -2.0297831425771921486916100519977404266947748691416922167961096320991761190057145636867796238254884443749e-56)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 4.8712635957157169685941764659378666193084431023269775678410920776942423498574161990151090862987707496709e-57)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -9.2547981414954593575052648297803007916203550348517241024188916829704035005537638171060497453987203484125e-58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 1.3442368462845102652888331895188311507347132911248615838604886657492687976498041391593065929847726694329e-58)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -1.4072191583666827552083642053400837423373421659342004966749178938352282349787956685790064733145823615594e-59)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, 9.4830105111768027064991929773116440103527225991506525293838437779387018237471847818347678097555938325901e-61)),
-         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 334, -3.0971820578438671326698299395846141298596444280876893045395714232857615676238866889122426000206260012404e-62)),
-      };
-      T result = 0;
-      T z = dz + 2;
-      for (unsigned k = 1; k <= sizeof(d) / sizeof(d[0]); ++k)
-      {
-         result += (-d[k - 1] * dz) / (z + k * z + k * k - 1);
-      }
-      return result;
-   }
-
-   static double g() { return 4.7377167968750001136868377216160297393798828125000000000000000000000000000000000000000000000000000000000e+01; }
-};
+   return 38.73733398437500;
+}
 
 
 //
@@ -3224,13 +2884,12 @@ struct lanczos
                 typename std::conditional<(target_precision <= lanczos17m64::value), lanczos17m64,
                 typename std::conditional<(target_precision <= lanczos24m113::value), lanczos24m113,
                 typename std::conditional<(target_precision <= lanczos22::value), lanczos22,
-                typename std::conditional<(target_precision <= lanczos32MP::value), lanczos32MP,
+                typename std::conditional<(target_precision <= lanczos27MP::value), lanczos27MP,
                 typename std::conditional<(target_precision <= lanczos35MP::value), lanczos35MP,
                 typename std::conditional<(target_precision <= lanczos48MP::value), lanczos48MP,
                 typename std::conditional<(target_precision <= lanczos49MP::value), lanczos49MP,
-                typename std::conditional<(target_precision <= lanczos49MP_2::value), lanczos49MP_2,
-                typename std::conditional<(target_precision <= lanczos58MP::value), lanczos58MP, undefined_lanczos>::type
-                >::type>::type>::type>::type>::type>::type>::type>::type>::type>::type
+                typename std::conditional<(target_precision <= lanczos52MP::value), lanczos52MP, undefined_lanczos>::type
+                >::type>::type>::type>::type>::type>::type>::type>::type>::type
                 >::type;
 };
 
@@ -3245,7 +2904,3 @@ struct lanczos
 #endif
 
 #endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS
-
-
-
-
diff --git a/tools/lanczos_generator.cpp b/tools/lanczos_generator.cpp
index 76b006b58..b026a7720 100644
--- a/tools/lanczos_generator.cpp
+++ b/tools/lanczos_generator.cpp
@@ -25,7 +25,7 @@
 // create a lanczos approximation for that type.
 //
 
-#define MP_TYPE boost::multiprecision::number<boost::multiprecision::cpp_bin_float<100> >
+#define MP_TYPE boost::multiprecision::number<boost::multiprecision::cpp_bin_float<90> >
 
 //
 // this is a sort of recursive include, since this file
@@ -4477,6 +4477,38 @@ lanczos_info<T> generate_lanczos(unsigned n, T g)
 
    return result;
 }
+
+template <class T>
+T lanczos_conditioning_near_1(const lanczos_info<T>& l)
+{
+   using std::abs;
+
+   T sum{ 0 };
+   T abs_sum{ 0 };
+
+   for (unsigned i = 1; i <= l.c.size(); ++i)
+   {
+      sum += l.c[i - 1] / (i * i);
+      abs_sum += abs(l.c[i - 1] / (i * i));
+   }
+   return abs(abs_sum / sum);
+}
+template <class T>
+T lanczos_conditioning_near_2(const lanczos_info<T>& l)
+{
+   using std::abs;
+
+   T sum{ 0 };
+   T abs_sum{ 0 };
+
+   for (unsigned i = 1; i <= l.c.size(); ++i)
+   {
+      sum += l.c[i - 1] / (i * i);
+      abs_sum += abs(l.c[i - 1] / (1 + 2 * i + i * i));
+   }
+   return abs(abs_sum / sum);
+}
+
 //
 // Stopwatch for measuring performance:
 //
@@ -4520,7 +4552,9 @@ std::vector<std::vector<T> > const & get_test_data()
          data.back().push_back(static_cast<T>(fact));
          data.back().push_back(static_cast<T>(log(fact)));
          fact = fact * T(k++);
-      }while(k < 100);
+         if (k > 500)
+            break;
+      }while(std::numeric_limits<T>::max() / k > fact);
 
       fact = 0.5;
       mp_t srpi = sqrt(boost::math::constants::pi<mp_t>());
@@ -4532,7 +4566,7 @@ std::vector<std::vector<T> > const & get_test_data()
          data.back().push_back(static_cast<T>(log(fact*srpi)));
          fact *= mul;
          mul += 1;
-      }while(mul < 100);
+      }while(mul < k);
    }
 
    return data;
@@ -5019,7 +5053,7 @@ void find_best_lanczos(const char* name, T eps, int max_scan = 100)
       lanczos_info<mp_t> best;
       best.err = 100; // best case had better be better than this!
 
-      std::cout << std::setw(20) << std::right << "N" << std::setw(20) << std::right << "g" << std::setw(20) << std::right << "eps" << std::setw(20) << std::right << "time (ms)\n";
+      std::cout << std::setw(20) << std::right << "N" << std::setw(20) << std::right << "g" << std::setw(20) << std::right << "eps" << std::setw(20) << std::right << "c at 1" << std::setw(20) << std::right << "c at 2" << std::setw(20) << std::right << "time (ms)\n";
 
       for (int i = 0; i < sizeof(sweet_spots) / sizeof(sweet_spots[0]); ++i)
       {
@@ -5031,8 +5065,11 @@ void find_best_lanczos(const char* name, T eps, int max_scan = 100)
             {
                std::cout << std::setprecision(14) << std::fixed << std::setw(20) << std::right << sweet_spots[i].N
                   << std::setw(20) << std::right << sweet_spots[i].g << std::setw(20) << std::right << static_cast<int>(err / eps)
+                  << std::setw(20) << std::right << (unsigned)lanczos_conditioning_near_1(info) << std::setw(20) << std::right << (unsigned)lanczos_conditioning_near_2(info)
                   << std::setw(20) << std::right << (int)(exec_time * 1000) << std::endl;
             }
+            else
+               std::cout << "Skipping spot with error: " << std::setprecision(5) << err << std::endl;
             if (err < best.err)
             {
                best = info;
@@ -5042,7 +5079,7 @@ void find_best_lanczos(const char* name, T eps, int max_scan = 100)
       }
       std::cout << std::endl;
 
-      if (best.err < 100)
+      if (best.err / eps < 100)
          print_code(best, name, std::numeric_limits<T>::max_digits10, std::numeric_limits<T>::digits);
       else
          std::cout << "Sorry, no viable approximation was found!!" << std::endl;

From c0afe2763a818c0cf1e25421ee7f2ab74e34c4c3 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 24 May 2021 10:11:53 +0100
Subject: [PATCH 4/5] Adjust tgamma error rates to new approximations. Mostly
 downward, but one slightly up.

---
 test/test_gamma_mp.cpp | 34 +++++++++++++++++-----------------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/test/test_gamma_mp.cpp b/test/test_gamma_mp.cpp
index b11faa91a..e11d69fd2 100644
--- a/test/test_gamma_mp.cpp
+++ b/test/test_gamma_mp.cpp
@@ -121,20 +121,6 @@ void expected_results()
    // Define the max and mean errors expected for
    // various compilers and platforms.
    //
-   add_expected_result(
-      ".*",                          // compiler
-      ".*",                          // stdlib
-      ".*",                          // platform
-      "number<cpp_bin_float<65> >",           // test type(s)
-      ".*",                          // test data group
-      "lgamma", 9000, 4000);      // test function
-   add_expected_result(
-      ".*",                          // compiler
-      ".*",                          // stdlib
-      ".*",                          // platform
-      "number<cpp_bin_float<75> >",           // test type(s)
-      ".*",                          // test data group
-      "lgamma", 60000, 20000);      // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
@@ -146,16 +132,30 @@ void expected_results()
       ".*",                          // compiler
       ".*",                          // stdlib
       ".*",                          // platform
-      ".*",                          // test type(s)
+      "number<cpp_bin_float<[56]5> >",           // test type(s)
       ".*",                          // test data group
-      "lgamma", 4800, 2500);           // test function
+      "lgamma", 7000, 3000);      // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "number<cpp_bin_float<75> >",           // test type(s)
+      ".*",                          // test data group
+      "lgamma", 40000, 15000);      // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
       ".*",                          // platform
       ".*",                          // test type(s)
       ".*",                          // test data group
-      "[tl]gamma", 100, 50);            // test function
+      "lgamma", 600, 200);            // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      "[tl]gamma", 120, 50);            // test function
    //
    // Finish off by printing out the compiler/stdlib/platform names,
    // we do this to make it easier to mark up expected error rates.

From 84b8e4ac81cc8bb68c01f2ba89fc84bf5c49d8f7 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 24 May 2021 13:20:45 +0100
Subject: [PATCH 5/5] Fix inspection report issues.

---
 tools/lanczos_generator.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tools/lanczos_generator.cpp b/tools/lanczos_generator.cpp
index b026a7720..e5c1c4e1b 100644
--- a/tools/lanczos_generator.cpp
+++ b/tools/lanczos_generator.cpp
@@ -4554,7 +4554,7 @@ std::vector<std::vector<T> > const & get_test_data()
          fact = fact * T(k++);
          if (k > 500)
             break;
-      }while(std::numeric_limits<T>::max() / k > fact);
+      }while((std::numeric_limits<T>::max)() / k > fact);
 
       fact = 0.5;
       mp_t srpi = sqrt(boost::math::constants::pi<mp_t>());