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
|
<!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 – Reference Manual: Legendre Form of Complete Elliptic Integrals</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Legendre Form of Complete Elliptic Integrals">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Legendre Form of Complete Elliptic Integrals">
<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="Elliptic-Integrals.html#Elliptic-Integrals" rel="up" title="Elliptic Integrals">
<link href="Legendre-Form-of-Incomplete-Elliptic-Integrals.html#Legendre-Form-of-Incomplete-Elliptic-Integrals" rel="next" title="Legendre Form of Incomplete Elliptic Integrals">
<link href="Definition-of-Carlson-Forms.html#Definition-of-Carlson-Forms" rel="previous" title="Definition of Carlson Forms">
<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="Legendre-Form-of-Complete-Elliptic-Integrals"></a>
<div class="header">
<p>
Next: <a href="Legendre-Form-of-Incomplete-Elliptic-Integrals.html#Legendre-Form-of-Incomplete-Elliptic-Integrals" accesskey="n" rel="next">Legendre Form of Incomplete Elliptic Integrals</a>, Previous: <a href="Definition-of-Carlson-Forms.html#Definition-of-Carlson-Forms" accesskey="p" rel="previous">Definition of Carlson Forms</a>, Up: <a href="Elliptic-Integrals.html#Elliptic-Integrals" accesskey="u" rel="up">Elliptic Integrals</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Legendre-Form-of-Complete-Elliptic-Integrals-1"></a>
<h4 class="subsection">7.13.3 Legendre Form of Complete Elliptic Integrals</h4>
<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fKcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Kcomp</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fKcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Kcomp_e</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>K(k)</em> to
the accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameter <em>m = k^2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fEcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Ecomp</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fEcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Ecomp_e</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>E(k)</em> to the
accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameter <em>m = k^2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fPcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Pcomp</strong> <em>(double <var>k</var>, double <var>n</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fPcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Pcomp_e</strong> <em>(double <var>k</var>, double <var>n</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>\Pi(k,n)</em> to the
accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameters <em>m = k^2</em> and <em>\sin^2(\alpha) = k^2</em>, with the
change of sign <em>n \to -n</em>.
</p></dd></dl>
</body>
</html>
|
