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// 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/special_functions/detail/bessel_jy_series.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)
{
BOOST_MATH_STD_USING
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 = static_cast<T>((n & 0x1) ? -1 : 1); // Y_{-n}(z) = (-1)^n Y_n(z)
n = -n;
}
else
{
factor = 1;
}
if(x < policies::get_epsilon<T, Policy>())
{
T scale = 1;
value = bessel_yn_small_z(n, x, &scale, pol);
if(tools::max_value<T>() * fabs(scale) < fabs(value))
return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
value /= scale;
}
else if(asymptotic_bessel_large_x_limit(n, x))
{
value = factor * asymptotic_bessel_y_large_x_2(static_cast<T>(abs(n)), x);
}
else 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);
policies::check_series_iterations<T>("boost::math::bessel_y_n<%1%>(%1%,%1%)", n, pol);
T mult = 2 * k / x;
value = mult * current - prev;
prev = current;
current = value;
++k;
if((mult > 1) && (fabs(current) > 1))
{
prev /= current;
factor /= current;
value /= current;
current = 1;
}
while(k < n)
{
mult = 2 * k / x;
value = mult * current - prev;
prev = current;
current = value;
++k;
}
if(fabs(tools::max_value<T>() * factor) < fabs(value))
return sign(value) * sign(factor) * policies::raise_overflow_error<T>(function, 0, pol);
value /= factor;
}
return value;
}
}}} // namespaces
#endif // BOOST_MATH_BESSEL_YN_HPP
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