1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections and no cover texts. A copy of the license is
included in the section entitled "GNU Free Documentation License". -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library – Reference Manual: Irregular Spherical Bessel Functions</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Irregular Spherical Bessel Functions">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Irregular Spherical Bessel Functions">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Bessel-Functions.html#Bessel-Functions" rel="up" title="Bessel Functions">
<link href="Regular-Modified-Spherical-Bessel-Functions.html#Regular-Modified-Spherical-Bessel-Functions" rel="next" title="Regular Modified Spherical Bessel Functions">
<link href="Regular-Spherical-Bessel-Functions.html#Regular-Spherical-Bessel-Functions" rel="previous" title="Regular Spherical Bessel Functions">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Irregular-Spherical-Bessel-Functions"></a>
<div class="header">
<p>
Next: <a href="Regular-Modified-Spherical-Bessel-Functions.html#Regular-Modified-Spherical-Bessel-Functions" accesskey="n" rel="next">Regular Modified Spherical Bessel Functions</a>, Previous: <a href="Regular-Spherical-Bessel-Functions.html#Regular-Spherical-Bessel-Functions" accesskey="p" rel="previous">Regular Spherical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Irregular-Spherical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.6 Irregular Spherical Bessel Functions</h4>
<a name="index-Irregular-Spherical-Bessel-Functions"></a>
<a name="index-y_0028x_0029_002c-Bessel-Functions"></a>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy0"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of zeroth
order, <em>y_0(x) = -\cos(x)/x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy1"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of first
order, <em>y_1(x) = -(\cos(x)/x + \sin(x))/x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy2"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of second
order, <em>y_2(x) = (-3/x^3 + 1/x)\cos(x) - (3/x^2)\sin(x)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl"></a>Function: <em>double</em> <strong>gsl_sf_bessel_yl</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_yl_e</strong> <em>(int <var>l</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of
order <var>l</var>, <em>y_l(x)</em>, for <em>l >= 0</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_yl_array</strong> <em>(int <var>lmax</var>, double <var>x</var>, double <var>result_array</var>[])</em></dt>
<dd><p>This routine computes the values of the irregular spherical Bessel
functions <em>y_l(x)</em> for <em>l</em> from 0 to <var>lmax</var>
inclusive for <em>lmax >= 0</em>, storing the results in the array <var>result_array</var>.
The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
</p></dd></dl>
</body>
</html>
|
