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
|
<html lang="en">
<head>
<title>Irregular Spherical Bessel Functions - GNU Scientific Library -- Reference Manual</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="GNU Scientific Library -- Reference Manual">
<meta name="generator" content="makeinfo 4.8">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Bessel-Functions.html" title="Bessel Functions">
<link rel="prev" href="Regular-Spherical-Bessel-Functions.html" title="Regular Spherical Bessel Functions">
<link rel="next" href="Regular-Modified-Spherical-Bessel-Functions.html" title="Regular Modified Spherical Bessel Functions">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<!--
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
Invariant Sections being ``GNU General Public License'' and ``Free Software
Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled ``GNU Free Documentation
License''.
(a) The Back-Cover Text is: ``You have freedom to copy and modify this
GNU Manual, like GNU software.''-->
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Irregular-Spherical-Bessel-Functions"></a>
Next: <a rel="next" accesskey="n" href="Regular-Modified-Spherical-Bessel-Functions.html">Regular Modified Spherical Bessel Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Regular-Spherical-Bessel-Functions.html">Regular Spherical Bessel Functions</a>,
Up: <a rel="up" accesskey="u" href="Bessel-Functions.html">Bessel Functions</a>
<hr>
</div>
<h4 class="subsection">7.5.6 Irregular Spherical Bessel Functions</h4>
<p><a name="index-Irregular-Spherical-Bessel-Functions-329"></a>
<div class="defun">
— Function: double <b>gsl_sf_bessel_y0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy0-330"></a></var><br>
— Function: int <b>gsl_sf_bessel_y0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy0_005fe-331"></a></var><br>
<blockquote><p>These routines compute the irregular spherical Bessel function of zeroth
order, y_0(x) = -\cos(x)/x.
<!-- Exceptional Return Values: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_y1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy1-332"></a></var><br>
— Function: int <b>gsl_sf_bessel_y1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy1_005fe-333"></a></var><br>
<blockquote><p>These routines compute the irregular spherical Bessel function of first
order, y_1(x) = -(\cos(x)/x + \sin(x))/x.
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_y2</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy2-334"></a></var><br>
— Function: int <b>gsl_sf_bessel_y2_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fy2_005fe-335"></a></var><br>
<blockquote><p>These routines compute the irregular spherical Bessel function of second
order, y_2(x) = (-3/x^3 + 1/x)\cos(x) - (3/x^2)\sin(x).
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_yl</b> (<var>int l, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fyl-336"></a></var><br>
— Function: int <b>gsl_sf_bessel_yl_e</b> (<var>int l, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fyl_005fe-337"></a></var><br>
<blockquote><p>These routines compute the irregular spherical Bessel function of
order <var>l</var>, y_l(x), for <!-- {$l \geq 0$} -->
l >= 0.
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_bessel_yl_array</b> (<var>int lmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fyl_005farray-338"></a></var><br>
<blockquote><p>This routine computes the values of the irregular spherical Bessel
functions y_l(x) for l from 0 to <var>lmax</var>
inclusive for <!-- {$lmax \geq 0$} -->
lmax >= 0, 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.
<!-- Domain: lmax >= 0 -->
<!-- Conditions: l=0,1,...,lmax -->
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<hr>The GNU Scientific Library - a free numerical library licensed under the GNU GPL<br>Back to the <a href="/software/gsl/">GNU Scientific Library Homepage</a></body></html>
|
