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
112
113
114
115
116
117
118
119
|
<html lang="en">
<head>
<title>Regular 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="Irregular-Modified-Cylindrical-Bessel-Functions.html" title="Irregular Modified Cylindrical Bessel Functions">
<link rel="next" href="Irregular-Spherical-Bessel-Functions.html" title="Irregular 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="Regular-Spherical-Bessel-Functions"></a>
Next: <a rel="next" accesskey="n" href="Irregular-Spherical-Bessel-Functions.html">Irregular Spherical Bessel Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Irregular-Modified-Cylindrical-Bessel-Functions.html">Irregular Modified Cylindrical Bessel Functions</a>,
Up: <a rel="up" accesskey="u" href="Bessel-Functions.html">Bessel Functions</a>
<hr>
</div>
<h4 class="subsection">7.5.5 Regular Spherical Bessel Functions</h4>
<p><a name="index-Spherical-Bessel-Functions-317"></a><a name="index-Regular-Spherical-Bessel-Functions-318"></a>
<div class="defun">
— Function: double <b>gsl_sf_bessel_j0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj0-319"></a></var><br>
— Function: int <b>gsl_sf_bessel_j0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj0_005fe-320"></a></var><br>
<blockquote><p>These routines compute the regular spherical Bessel function of zeroth
order, j_0(x) = \sin(x)/x.
<!-- Exceptional Return Values: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_j1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj1-321"></a></var><br>
— Function: int <b>gsl_sf_bessel_j1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj1_005fe-322"></a></var><br>
<blockquote><p>These routines compute the regular spherical Bessel function of first
order, j_1(x) = (\sin(x)/x - \cos(x))/x.
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_j2</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj2-323"></a></var><br>
— Function: int <b>gsl_sf_bessel_j2_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fj2_005fe-324"></a></var><br>
<blockquote><p>These routines compute the regular spherical Bessel function of second
order, j_2(x) = ((3/x^2 - 1)\sin(x) - 3\cos(x)/x)/x.
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_jl</b> (<var>int l, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fjl-325"></a></var><br>
— Function: int <b>gsl_sf_bessel_jl_e</b> (<var>int l, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fjl_005fe-326"></a></var><br>
<blockquote><p>These routines compute the regular spherical Bessel function of
order <var>l</var>, j_l(x), for <!-- {$l \geq 0$} -->
l >= 0 and <!-- {$x \geq 0$} -->
x >= 0.
<!-- Domain: l >= 0, x >= 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_bessel_jl_array</b> (<var>int lmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fjl_005farray-327"></a></var><br>
<blockquote><p>This routine computes the values of the regular spherical Bessel
functions j_l(x) for l from 0 to <var>lmax</var>
inclusive for <!-- {$lmax \geq 0$} -->
lmax >= 0 and <!-- {$x \geq 0$} -->
x >= 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_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_bessel_jl_steed_array</b> (<var>int lmax, double x, double * jl_x_array</var>)<var><a name="index-gsl_005fsf_005fbessel_005fjl_005fsteed_005farray-328"></a></var><br>
<blockquote><p>This routine uses Steed's method to compute the values of the regular
spherical Bessel functions j_l(x) for l from 0 to
<var>lmax</var> inclusive for <!-- {$lmax \geq 0$} -->
lmax >= 0 and <!-- {$x \geq 0$} -->
x >= 0, storing the results in the array
<var>result_array</var>.
The Steed/Barnett algorithm is described in <cite>Comp. Phys. Comm.</cite> 21,
297 (1981). Steed's method is more stable than the
recurrence used in the other functions but is also slower.
<!-- Domain: lmax >= 0 -->
<!-- Conditions: l=0,1,...,lmax -->
<!-- Exceptional Return Values: GSL_EDOM, 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>
|
