// 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_YN_HPP | |
#define BOOST_MATH_BESSEL_YN_HPP | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/math/special_functions/detail/bessel_y0.hpp> | |
#include <boost/math/special_functions/detail/bessel_y1.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
// Bessel function of the second kind of integer order | |
// Y_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_yn(int n, T x, const Policy& pol) | |
{ | |
T value, factor, current, prev; | |
using namespace boost::math::tools; | |
static const char* function = "boost::math::bessel_yn<%1%>(%1%,%1%)"; | |
if ((x == 0) && (n == 0)) | |
{ | |
return -policies::raise_overflow_error<T>(function, 0, pol); | |
} | |
if (x <= 0) | |
{ | |
return policies::raise_domain_error<T>(function, | |
"Got x = %1%, but x must be > 0, complex result not supported.", x, pol); | |
} | |
// | |
// Reflection comes first: | |
// | |
if (n < 0) | |
{ | |
factor = (n & 0x1) ? -1 : 1; // Y_{-n}(z) = (-1)^n Y_n(z) | |
n = -n; | |
} | |
else | |
{ | |
factor = 1; | |
} | |
if (n == 0) | |
{ | |
value = bessel_y0(x, pol); | |
} | |
else if (n == 1) | |
{ | |
value = factor * bessel_y1(x, pol); | |
} | |
else | |
{ | |
prev = bessel_y0(x, pol); | |
current = bessel_y1(x, pol); | |
int k = 1; | |
BOOST_ASSERT(k < n); | |
do | |
{ | |
value = 2 * k * current / x - prev; | |
prev = current; | |
current = value; | |
++k; | |
} | |
while(k < n); | |
value *= factor; | |
} | |
return value; | |
} | |
}}} // namespaces | |
#endif // BOOST_MATH_BESSEL_YN_HPP | |