--- /dev/null
+// 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 = (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 (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);
+ do
+ {
+ T fact = 2 * k / x;
+ if((fact > 1) && ((tools::max_value<T>() - fabs(prev)) / fact < fabs(current)))
+ {
+ prev /= current;
+ factor /= current;
+ current = 1;
+ }
+ value = fact * current - prev;
+ prev = current;
+ current = value;
+ ++k;
+ }
+ while(k < n);
+ if(fabs(tools::max_value<T>() * factor) < fabs(value))
+ return sign(value) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
+ value /= factor;
+ }
+ return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_YN_HPP
+