1// Copyright (c) 2006 Xiaogang Zhang
2// Use, modification and distribution are subject to the
3// Boost Software License, Version 1.0. (See accompanying file
4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6#ifndef BOOST_MATH_BESSEL_YN_HPP
7#define BOOST_MATH_BESSEL_YN_HPP
8
9#ifdef _MSC_VER
10#pragma once
11#endif
12
13#include <boost/math/special_functions/detail/bessel_y0.hpp>
14#include <boost/math/special_functions/detail/bessel_y1.hpp>
15#include <boost/math/special_functions/detail/bessel_jy_series.hpp>
16#include <boost/math/policies/error_handling.hpp>
17
18// Bessel function of the second kind of integer order
19// Y_n(z) is the dominant solution, forward recurrence always OK (though unstable)
20
21namespace boost { namespace math { namespace detail{
22
23template <typename T, typename Policy>
24T bessel_yn(int n, T x, const Policy& pol)
25{
26 BOOST_MATH_STD_USING
27 T value, factor, current, prev;
28
29 using namespace boost::math::tools;
30
31 static const char* function = "boost::math::bessel_yn<%1%>(%1%,%1%)";
32
33 if ((x == 0) && (n == 0))
34 {
35 return -policies::raise_overflow_error<T>(function, 0, pol);
36 }
37 if (x <= 0)
38 {
39 return policies::raise_domain_error<T>(function,
40 "Got x = %1%, but x must be > 0, complex result not supported.", x, pol);
41 }
42
43 //
44 // Reflection comes first:
45 //
46 if (n < 0)
47 {
48 factor = static_cast<T>((n & 0x1) ? -1 : 1); // Y_{-n}(z) = (-1)^n Y_n(z)
49 n = -n;
50 }
51 else
52 {
53 factor = 1;
54 }
55 if(x < policies::get_epsilon<T, Policy>())
56 {
57 T scale = 1;
58 value = bessel_yn_small_z(n, x, &scale, pol);
59 if(tools::max_value<T>() * fabs(scale) < fabs(value))
60 return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
61 value /= scale;
62 }
63 else if(asymptotic_bessel_large_x_limit(n, x))
64 {
65 value = factor * asymptotic_bessel_y_large_x_2(static_cast<T>(abs(n)), x);
66 }
67 else if (n == 0)
68 {
69 value = bessel_y0(x, pol);
70 }
71 else if (n == 1)
72 {
73 value = factor * bessel_y1(x, pol);
74 }
75 else
76 {
77 prev = bessel_y0(x, pol);
78 current = bessel_y1(x, pol);
79 int k = 1;
80 BOOST_ASSERT(k < n);
81 policies::check_series_iterations<T>("boost::math::bessel_y_n<%1%>(%1%,%1%)", n, pol);
82 T mult = 2 * k / x;
83 value = mult * current - prev;
84 prev = current;
85 current = value;
86 ++k;
87 if((mult > 1) && (fabs(current) > 1))
88 {
89 prev /= current;
90 factor /= current;
91 value /= current;
92 current = 1;
93 }
94 while(k < n)
95 {
96 mult = 2 * k / x;
97 value = mult * current - prev;
98 prev = current;
99 current = value;
100 ++k;
101 }
102 if(fabs(tools::max_value<T>() * factor) < fabs(value))
103 return sign(value) * sign(factor) * policies::raise_overflow_error<T>(function, 0, pol);
104 value /= factor;
105 }
106 return value;
107}
108
109}}} // namespaces
110
111#endif // BOOST_MATH_BESSEL_YN_HPP
112
113

source code of include/boost/math/special_functions/detail/bessel_yn.hpp