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///////////////////////////////////////////////////////////////////////////////
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// Copyright 2018 John Maddock
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// Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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//
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#ifndef BOOST_MATH_HYPERGEOMETRIC_1F1_CF_HPP
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#define BOOST_MATH_HYPERGEOMETRIC_1F1_CF_HPP
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//
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// Evaluation of 1F1 by continued fraction
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// by asymptotic approximation for large a,
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// see https://dlmf.nist.gov/13.8#E9
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//
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// This is not terribly useful, as it only gets a few digits correct even for very
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// large a, also needs b and z small:
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//
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namespace boost { namespace math { namespace detail {
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template <class T, class Policy>
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T hypergeometric_1F1_large_neg_a_asymtotic_dlmf_13_8_9(T a, T b, T z, const Policy& pol)
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{
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T result = boost::math::cyl_bessel_j(b - 1, sqrt(2 * z * (b - 2 * a)), pol);
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result *= boost::math::tgamma(b, pol) * exp(z / 2);
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T p = pow((b / 2 - a) * z, (1 - b) / 4);
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result *= p;
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result *= p;
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return result;
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}
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} } } // namespaces
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#endif // BOOST_MATH_HYPERGEOMETRIC_1F1_BESSEL_HPP
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