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Filename : hypergeometric_1F1_cf.hpp
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///////////////////////////////////////////////////////////////////////////////
//  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

#include <boost/math/tools/fraction.hpp>

//
// Evaluation of 1F1 by continued fraction
// see http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/10/0002/
//
// This is not terribly useful, as like the series we're adding a something to 1,
// so only really useful when we know that the result will be > 1.
//


  namespace boost { namespace math { namespace detail {

     template <class T>
     struct hypergeometric_1F1_cf_func
     {
        typedef std::pair<T, T>  result_type;
        hypergeometric_1F1_cf_func(T a_, T b_, T z_) : a(a_), b(b_), z(z_), k(0) {}
        std::pair<T, T> operator()()
        {
           ++k;
           return std::make_pair(-(((a + k) * z) / ((k + 1) * (b + k))), 1 + ((a + k) * z) / ((k + 1) * (b + k)));
        }
        T a, b, z;
        unsigned k;
     };

     template <class T, class Policy>
     T hypergeometric_1F1_cf(const T& a, const T& b, const T& z, const Policy& pol, const char* function)
     {
        hypergeometric_1F1_cf_func<T> func(a, b, z);
        boost::uintmax_t max_iter = boost::math::policies::get_max_series_iterations<Policy>();
        T result = boost::math::tools::continued_fraction_a(func, boost::math::policies::get_epsilon<T, Policy>(), max_iter);
        boost::math::policies::check_series_iterations<T>(function, max_iter, pol);
        return 1 + a * z / (b * (1 + result));
     }

  } } } // namespaces

#endif // BOOST_MATH_HYPERGEOMETRIC_1F1_BESSEL_HPP