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hypergeometric_1F1_large_a.hpp
/////////////////////////////////////////////////////////////////////////////// // Copyright 2018 John Maddock // Distributed under 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_HYPERGEOMETRIC_1F1_CF_HPP #define BOOST_MATH_HYPERGEOMETRIC_1F1_CF_HPP // // Evaluation of 1F1 by continued fraction // by asymptotic approximation for large a, // see https://dlmf.nist.gov/13.8#E9 // // This is not terribly useful, as it only gets a few digits correct even for very // large a, also needs b and z small: // namespace boost { namespace math { namespace detail { template <class T, class Policy> T hypergeometric_1F1_large_neg_a_asymtotic_dlmf_13_8_9(T a, T b, T z, const Policy& pol) { T result = boost::math::cyl_bessel_j(b - 1, sqrt(2 * z * (b - 2 * a)), pol); result *= boost::math::tgamma(b, pol) * exp(z / 2); T p = pow((b / 2 - a) * z, (1 - b) / 4); result *= p; result *= p; return result; } } } } // namespaces #endif // BOOST_MATH_HYPERGEOMETRIC_1F1_BESSEL_HPP
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