// Copyright (c) 2006 Xiaogang Zhang | |
// 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_BESSEL_KN_HPP | |
#define BOOST_MATH_BESSEL_KN_HPP | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/math/special_functions/detail/bessel_k0.hpp> | |
#include <boost/math/special_functions/detail/bessel_k1.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
// Modified Bessel function of the second kind of integer order | |
// K_n(z) is the dominant solution, forward recurrence always OK (though unstable) | |
namespace boost { namespace math { namespace detail{ | |
template <typename T, typename Policy> | |
T bessel_kn(int n, T x, const Policy& pol) | |
{ | |
T value, current, prev; | |
using namespace boost::math::tools; | |
static const char* function = "boost::math::bessel_kn<%1%>(%1%,%1%)"; | |
if (x < 0) | |
{ | |
return policies::raise_domain_error<T>(function, | |
"Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol); | |
} | |
if (x == 0) | |
{ | |
return policies::raise_overflow_error<T>(function, 0, pol); | |
} | |
if (n < 0) | |
{ | |
n = -n; // K_{-n}(z) = K_n(z) | |
} | |
if (n == 0) | |
{ | |
value = bessel_k0(x, pol); | |
} | |
else if (n == 1) | |
{ | |
value = bessel_k1(x, pol); | |
} | |
else | |
{ | |
prev = bessel_k0(x, pol); | |
current = bessel_k1(x, pol); | |
int k = 1; | |
BOOST_ASSERT(k < n); | |
do | |
{ | |
value = 2 * k * current / x + prev; | |
prev = current; | |
current = value; | |
++k; | |
} | |
while(k < n); | |
} | |
return value; | |
} | |
}}} // namespaces | |
#endif // BOOST_MATH_BESSEL_KN_HPP | |