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
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
|
<!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: Special Functions Examples</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Special Functions Examples">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Special Functions Examples">
<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="Special-Functions.html#Special-Functions" rel="up" title="Special Functions">
<link href="Special-Functions-References-and-Further-Reading.html#Special-Functions-References-and-Further-Reading" rel="next" title="Special Functions References and Further Reading">
<link href="Eta-Function.html#Eta-Function" rel="previous" title="Eta Function">
<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="Special-Functions-Examples"></a>
<div class="header">
<p>
Next: <a href="Special-Functions-References-and-Further-Reading.html#Special-Functions-References-and-Further-Reading" accesskey="n" rel="next">Special Functions References and Further Reading</a>, Previous: <a href="Zeta-Functions.html#Zeta-Functions" accesskey="p" rel="previous">Zeta Functions</a>, Up: <a href="Special-Functions.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Examples-2"></a>
<h3 class="section">7.33 Examples</h3>
<p>The following example demonstrates the use of the error handling form of
the special functions, in this case to compute the Bessel function
<em>J_0(5.0)</em>,
</p>
<div class="example">
<pre class="verbatim">#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_bessel.h>
int
main (void)
{
double x = 5.0;
gsl_sf_result result;
double expected = -0.17759677131433830434739701;
int status = gsl_sf_bessel_J0_e (x, &result);
printf ("status = %s\n", gsl_strerror(status));
printf ("J0(5.0) = %.18f\n"
" +/- % .18f\n",
result.val, result.err);
printf ("exact = %.18f\n", expected);
return status;
}
</pre></div>
<p>Here are the results of running the program,
</p>
<div class="example">
<pre class="example">$ ./a.out
</pre><pre class="verbatim">status = success
J0(5.0) = -0.177596771314338292
+/- 0.000000000000000193
exact = -0.177596771314338292
</pre></div>
<p>The next program computes the same quantity using the natural form of
the function. In this case the error term <var>result.err</var> and return
status are not accessible.
</p>
<div class="example">
<pre class="verbatim">#include <stdio.h>
#include <gsl/gsl_sf_bessel.h>
int
main (void)
{
double x = 5.0;
double expected = -0.17759677131433830434739701;
double y = gsl_sf_bessel_J0 (x);
printf ("J0(5.0) = %.18f\n", y);
printf ("exact = %.18f\n", expected);
return 0;
}
</pre></div>
<p>The results of the function are the same,
</p>
<div class="example">
<pre class="example">$ ./a.out
</pre><pre class="verbatim">J0(5.0) = -0.177596771314338292
exact = -0.177596771314338292
</pre></div>
</body>
</html>
|
