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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_HL_HPP
+#define BOOST_MATH_ELLINT_HL_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/ellint_rj.hpp>
+#include <boost/math/special_functions/ellint_rj.hpp>
+#include <boost/math/special_functions/ellint_1.hpp>
+#include <boost/math/special_functions/jacobi_zeta.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 heuman_lambda_imp(T phi, T k, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+ using namespace boost::math::constants;
+
+ const char* function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";
+
+ if(fabs(k) > 1)
+ return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);
+
+ T result;
+ T sinp = sin(phi);
+ T cosp = cos(phi);
+ T s2 = sinp * sinp;
+ T k2 = k * k;
+ T kp = 1 - k2;
+ T delta = sqrt(1 - (kp * s2));
+ if(fabs(phi) <= constants::half_pi<T>())
+ {
+ result = kp * sinp * cosp / (delta * constants::half_pi<T>());
+ result *= ellint_rf_imp(T(0), kp, T(1), pol) + k2 * ellint_rj(T(0), kp, T(1), T(1 - k2 / (delta * delta)), pol) / (3 * delta * delta);
+ }
+ else
+ {
+ T rkp = sqrt(kp);
+ T ratio;
+ if(rkp == 1)
+ {
+ return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);
+ }
+ else
+ ratio = ellint_f_imp(phi, rkp, pol) / ellint_k_imp(rkp, pol);
+ result = ratio + ellint_k_imp(k, pol) * jacobi_zeta_imp(phi, rkp, pol) / constants::half_pi<T>();
+ }
+ return result;
+}
+
+} // detail
+
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type heuman_lambda(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::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi)
+{
+ return boost::math::heuman_lambda(k, phi, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_D_HPP
+