File: Regular-Modified-Spherical-Bessel-Functions.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (123 lines) | stat: -rw-r--r-- 7,142 bytes parent folder | download
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
120
121
122
123
<!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, 2014, 2015, 2016 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 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 the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: Regular Modified Spherical Bessel Functions</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Regular Modified Spherical Bessel Functions">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Regular Modified 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="Irregular-Modified-Spherical-Bessel-Functions.html#Irregular-Modified-Spherical-Bessel-Functions" rel="next" title="Irregular Modified Spherical Bessel Functions">
<link href="Irregular-Spherical-Bessel-Functions.html#Irregular-Spherical-Bessel-Functions" rel="previous" title="Irregular 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="Regular-Modified-Spherical-Bessel-Functions"></a>
<div class="header">
<p>
Next: <a href="Irregular-Modified-Spherical-Bessel-Functions.html#Irregular-Modified-Spherical-Bessel-Functions" accesskey="n" rel="next">Irregular Modified Spherical Bessel Functions</a>, Previous: <a href="Irregular-Spherical-Bessel-Functions.html#Irregular-Spherical-Bessel-Functions" accesskey="p" rel="previous">Irregular Spherical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Regular-Modified-Spherical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.7 Regular Modified Spherical Bessel Functions</h4>
<a name="index-Modified-Spherical-Bessel-Functions"></a>
<a name="index-Regular-Modified-Spherical-Bessel-Functions"></a>
<a name="index-i_0028x_0029_002c-Bessel-Functions"></a>

<p>The regular modified spherical Bessel functions <em>i_l(x)</em> 
are related to the modified Bessel functions of fractional order,
<em>i_l(x) = \sqrt{\pi/(2x)} I_{l+1/2}(x)</em>
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fi0_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_i0_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fi0_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_i0_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled regular modified spherical Bessel
function of zeroth order, <em>\exp(-|x|) i_0(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fi1_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_i1_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fi1_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_i1_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled regular modified spherical Bessel
function of first order, <em>\exp(-|x|) i_1(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fi2_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_i2_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fi2_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_i2_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled regular modified spherical Bessel
function of second order, <em>\exp(-|x|) i_2(x) </em> 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fil_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_il_scaled</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fil_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_il_scaled_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 scaled regular modified spherical Bessel
function of order <var>l</var>, <em>\exp(-|x|) i_l(x) </em>
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fil_005fscaled_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_il_scaled_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 scaled regular modified
spherical Bessel functions <em>\exp(-|x|) i_l(x)</em> for <em>l</em> from
0 to <var>lmax</var> inclusive for <em>lmax &gt;= 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>