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+// Copyright (c) 2015 John Maddock
+// 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)
+//
+
+#ifndef BOOST_MATH_ELLINT_JZ_HPP
+#define BOOST_MATH_ELLINT_JZ_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/ellint_1.hpp>
+#include <boost/math/special_functions/ellint_rj.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/tools/workaround.hpp>
+
+// Elliptic integral the Jacobi Zeta function.
+
+namespace boost { namespace math {
+
+namespace detail{
+
+// Elliptic integral - Jacobi Zeta
+template <typename T, typename Policy>
+T jacobi_zeta_imp(T phi, T k, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+ using namespace boost::math::constants;
+
+ bool invert = false;
+ if(phi < 0)
+ {
+ phi = fabs(phi);
+ invert = true;
+ }
+
+ T result;
+ T sinp = sin(phi);
+ T cosp = cos(phi);
+ T s2 = sinp * sinp;
+ T k2 = k * k;
+ T kp = 1 - k2;
+ if(k == 1)
+ result = sinp * (boost::math::sign)(cosp); // We get here by simplifying JacobiZeta[w, 1] in Mathematica, and the fact that 0 <= phi.
+ else
+ result = k2 * sinp * cosp * sqrt(1 - k2 * s2) * ellint_rj_imp(T(0), kp, T(1), T(1 - k2 * s2), pol) / (3 * ellint_k_imp(k, pol));
+ return invert ? T(-result) : result;
+}
+
+} // detail
+
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(detail::jacobi_zeta_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::jacobi_zeta<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi)
+{
+ return boost::math::jacobi_zeta(k, phi, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_D_HPP
+