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1F1: Fix documentation typos.

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jzmaddock
2019-08-03 10:11:38 +01:00
parent f3eafa4d34
commit 9350bda2bd
2 changed files with 6 additions and 6 deletions
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4
doc/internals/recurrence.qbk
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@@ -67,7 +67,7 @@ Given a functor r which encodes the recurrence relation for function F at some l
[/\Large $$ F_n / F_{n-1} $$][$../equations/three_term_recurrence_backwards_ratio.svg]
This calculation is stable only if recurrence is stable in the backwards direction. Further the ration calculated
This calculation is stable only if recurrence is stable in the backwards direction. Further the ratio calculated
is for the dominant solution (in the backwards direction) of the recurrence relation, if there are multiple solutions,
then there is no guarantee that this will find the one you want or expect.
@@ -82,7 +82,7 @@ Given a functor r which encodes the recurrence relation for function F at some l
[/\Large $$ F_n / F_{n+1} $$][$../equations/three_term_recurrence_forwards_ratio.svg]
This calculation is stable only if recurrence is stable in the forwards direction. Further the ration calculated
This calculation is stable only if recurrence is stable in the forwards direction. Further the ratio calculated
is for the dominant solution (in the forwards direction) of the recurrence relation, if there are multiple solutions,
then there is no guarantee that this will find the one you want or expect.

8
doc/sf/hypergeometric.qbk
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@@ -230,7 +230,7 @@ We also have a [@../../tools/hypergeometric_1F1_error_plot.cpp small program] fo
is also used for the error rate plots below and has been extremely useful in fine tuning the implementation.
It should be noted however, that there are some domains for large negative /a/ and /b/ that have poor test coverage as we were
simply unable to compute test values in reasonable time: it is not uncommon for the /pFq/ series to cancel many humdreds of digits
simply unable to compute test values in reasonable time: it is not uncommon for the /pFq/ series to cancel many hundreds of digits
and sometimes into the thousands of digits.
[h4 Errors]
@@ -401,10 +401,10 @@ For /b < 0/ we have no good methods in some domains (see the unsolved issues abo
However in some circumstances we can either use:
* 3-stage backwards recursion on both /a/, /a/ and /b/ and then /b/ as above.
* Calculate the ratio ['[sub 1]F[sub 1](a, b, z) / ['[sub 1]F[sub 1](a-1, b-1, z)]] via backwards recurence when z is small, and then normalize via the Wronskian above (Miller's method).
* Calculate the ratio ['[sub 1]F[sub 1](a, b, z) / ['[sub 1]F[sub 1](a+1, b+1, z)]] via forwards recurence when z is large, and then normalize by iterating until b > 1 and comparing to a reference value.
* Calculate the ratio ['[sub 1]F[sub 1](a, b, z) / ['[sub 1]F[sub 1](a-1, b-1, z)]] via backwards recurrence when z is small, and then normalize via the Wronskian above (Miller's method).
* Calculate the ratio ['[sub 1]F[sub 1](a, b, z) / ['[sub 1]F[sub 1](a+1, b+1, z)]] via forwards recurrence when z is large, and then normalize by iterating until b > 1 and comparing to a reference value.
The latter two methods use a lookup table to detrmine whether inputs are in either of the domains or neither. Unfortunately the methods are basically
The latter two methods use a lookup table to determine whether inputs are in either of the domains or neither. Unfortunately the methods are basically
limited to double precision: calculation of the ratios require iteration ['towards] the no-mans-land between the two methods where iteration is unstable in
both directions. As a result, only low-precision results which require few iterations to calculate the ratio are available.