diff --git a/include/boost/math/special_functions/jacobi.hpp b/include/boost/math/special_functions/jacobi.hpp
index 6451ce978..4c744af2f 100644
--- a/include/boost/math/special_functions/jacobi.hpp
+++ b/include/boost/math/special_functions/jacobi.hpp
@@ -37,5 +37,19 @@ Real jacobi(unsigned n, Real alpha, Real beta, Real x)
     return yk;
 }
 
+template<typename Real>
+Real jacobi_derivative(unsigned n, Real alpha, Real beta, Real x, unsigned k)
+{
+    if (k > n) {
+        return Real(0);
+    }
+    Real scale = 1;
+    for(unsigned j = 1; j <= k; ++j) {
+        scale *= (alpha + beta + n + j)/2;
+    }
+
+    return scale*jacobi<Real>(n-k, alpha + k, beta+k, x);
+}
+
 }}
 #endif
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 53905d8d1..bf76ce0e0 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -939,6 +939,7 @@ test-suite misc :
    [ run test_vector_barycentric_rational.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx11_smart_ptr cxx11_defaulted_functions cxx11_auto_declarations cxx11_unified_initialization_syntax ]  [ check-target-builds ../../multiprecision/config//has_eigen : : <build>no ] ]
    [ run test_cubic_b_spline.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx11_smart_ptr cxx11_defaulted_functions ] <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release ]
    [ run cardinal_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=1 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_1 ]
diff --git a/test/jacobi_test.cpp b/test/jacobi_test.cpp
new file mode 100644
index 000000000..2a3d52f9d
--- /dev/null
+++ b/test/jacobi_test.cpp
@@ -0,0 +1,118 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <random>
+#include <cmath>
+#include <boost/math/special_functions/jacobi.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+using std::abs;
+using boost::math::jacobi;
+using boost::math::jacobi_derivative;
+
+template<typename Real>
+void test_to_quadratic()
+{
+    Real h = 1/Real(8);
+    for (Real alpha = -1 + h; alpha < 2; alpha += h) {
+        for (Real beta = -1 + h; beta < 2; beta += h) {
+            for (Real x = -1; x < 1; x += h) {
+                Real expected = 1;
+                Real computed = jacobi(0, alpha, beta, x);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+
+                expected = (alpha + 1) + (alpha + beta +2)*(x-1)/2;
+                computed = jacobi(1, alpha, beta, x);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+
+                expected = (alpha + 1)*(alpha+2)/2 + (alpha + 2)*(alpha + beta + 3)*(x-1)/2 + (alpha + beta + 3)*(alpha + beta + 4)*(x-1)*(x-1)/8;
+                computed = jacobi(2, alpha, beta, x);
+                CHECK_ULP_CLOSE(expected, computed, 1);
+
+            }
+        }
+    }
+}
+
+template<typename Real>
+void test_symmetry()
+{
+    Real h = 1/Real(4);
+    for (Real alpha = -1 + h; alpha < 2; alpha += h) {
+        for (Real beta = -1 + h; beta < 2; beta += h) {
+            for (Real x = -1; x < 1; x += h) {
+                for (size_t n = 0; n < 20; n += 2)
+                {
+                    Real expected = jacobi(n, beta, alpha , -x);
+                    Real computed = jacobi(n, alpha, beta, x);
+                    CHECK_ULP_CLOSE(expected, computed, 0);
+
+                    expected = jacobi(n+1, beta, alpha, -x);
+                    computed = -jacobi(n+1, alpha, beta, x);
+                    CHECK_ULP_CLOSE(expected, computed, 0);
+                }
+            }
+        }
+    }
+}
+
+template<typename Real>
+void test_derivative()
+{
+    Real h = 1/Real(4);
+    for (Real alpha = -1 + h; alpha < 2; alpha += h) {
+        for (Real beta = -1 + h; beta < 2; beta += h) {
+            for (Real x = -1; x < 1; x += h) {
+                Real expected = 0;
+                Real computed = jacobi_derivative(0, alpha, beta, x, 1);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+
+                expected = (alpha + beta + 2)/2;
+                computed = jacobi_derivative(1, alpha, beta, x, 1);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+
+                expected = (alpha + 2)*(alpha + beta + 3)/2 + (alpha + beta + 3)*(alpha + beta + 4)*(x-1)/4;
+                computed = jacobi_derivative(2, alpha, beta, x, 1);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+
+                expected = (alpha + beta + 3)*(alpha + beta + 4)/4;
+                computed = jacobi_derivative(2, alpha, beta, x, 2);
+                CHECK_ULP_CLOSE(expected, computed, 0);
+            }
+        }
+    }
+}
+
+int main()
+{
+
+    test_to_quadratic<float>();
+    test_to_quadratic<double>();
+    test_to_quadratic<long double>();
+
+    test_symmetry<float>();
+    test_symmetry<double>();
+    test_symmetry<long double>();
+
+    test_derivative<float>();
+    test_derivative<double>();
+    test_derivative<long double>();
+
+#ifdef BOOST_HAS_FLOAT128
+    test_to_quadratic<boost::multiprecision::float128>();
+    test_symmetry<boost::multiprecision::float128>();
+    test_derivative<boost::multiprecision::float128>();
+#endif
+
+    return boost::math::test::report_errors();
+}