///////////////////////////////////////////////////////////////////////////////
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// Copyright 2014 Anton Bikineev
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// Copyright 2014 Christopher Kormanyos
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// Copyright 2014 John Maddock
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// Copyright 2014 Paul Bristow
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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_SEPARATED_SERIES_HPP
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#define BOOST_MATH_HYPERGEOMETRIC_SEPARATED_SERIES_HPP
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namespace boost { namespace math { namespace detail {
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template <class T, class Policy>
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inline T hypergeometric_1F1_separated_series(const T& a, const T& b, const T& z, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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const T factor = policies::get_epsilon<T, Policy>();
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T denom = 1, numer = 1;
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T intermediate_result = 1, result = 1;
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T a_pochhammer = a, z_pow = z;
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unsigned N = 0;
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while (--max_iter)
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{
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++N;
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const T mult = (((b + N) - 1) * N);
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denom *= mult; numer *= mult;
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numer += a_pochhammer * z_pow;
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result = numer / denom;
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if (fabs(factor * result) > fabs(result - intermediate_result))
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break;
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intermediate_result = result;
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a_pochhammer *= (a + N);
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z_pow *= z;
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}
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return result;
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}
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} } } // namespaces
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#endif // BOOST_MATH_HYPERGEOMETRIC_SEPARATED_SERIES_HPP
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