File: Incomplete-Gamma-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 (108 lines) | stat: -rw-r--r-- 5,775 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
<!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: Incomplete Gamma Functions</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Incomplete Gamma Functions">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Incomplete Gamma 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="Gamma-and-Beta-Functions.html#Gamma-and-Beta-Functions" rel="up" title="Gamma and Beta Functions">
<link href="Beta-Functions.html#Beta-Functions" rel="next" title="Beta Functions">
<link href="Pochhammer-Symbol.html#Pochhammer-Symbol" rel="previous" title="Pochhammer Symbol">
<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="Incomplete-Gamma-Functions"></a>
<div class="header">
<p>
Next: <a href="Beta-Functions.html#Beta-Functions" accesskey="n" rel="next">Beta Functions</a>, Previous: <a href="Pochhammer-Symbol.html#Pochhammer-Symbol" accesskey="p" rel="previous">Pochhammer Symbol</a>, Up: <a href="Gamma-and-Beta-Functions.html#Gamma-and-Beta-Functions" accesskey="u" rel="up">Gamma and Beta Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Incomplete-Gamma-Functions-1"></a>
<h4 class="subsection">7.19.4 Incomplete Gamma Functions</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fgamma_005finc"></a>Function: <em>double</em> <strong>gsl_sf_gamma_inc</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fgamma_005finc_005fe"></a>Function: <em>int</em> <strong>gsl_sf_gamma_inc_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-non_002dnormalized-incomplete-Gamma-function"></a>
<a name="index-unnormalized-incomplete-Gamma-function"></a>
<p>These functions compute the unnormalized incomplete Gamma Function
<em>\Gamma(a,x) = \int_x^\infty dt t^{a-1} \exp(-t)</em>
for <em>a</em> real and <em>x &gt;= 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fgamma_005finc_005fQ"></a>Function: <em>double</em> <strong>gsl_sf_gamma_inc_Q</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fgamma_005finc_005fQ_005fe"></a>Function: <em>int</em> <strong>gsl_sf_gamma_inc_Q_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-incomplete-Gamma-function"></a>
<p>These routines compute the normalized incomplete Gamma Function
<em>Q(a,x) = 1/\Gamma(a) \int_x^\infty dt t^{a-1} \exp(-t)</em>
for <em>a &gt; 0</em>, <em>x &gt;= 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fgamma_005finc_005fP"></a>Function: <em>double</em> <strong>gsl_sf_gamma_inc_P</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fgamma_005finc_005fP_005fe"></a>Function: <em>int</em> <strong>gsl_sf_gamma_inc_P_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-complementary-incomplete-Gamma-function"></a>
<p>These routines compute the complementary normalized incomplete Gamma Function
<em>P(a,x) = 1 - Q(a,x) = 1/\Gamma(a) \int_0^x dt t^{a-1} \exp(-t)</em>
for <em>a &gt; 0</em>, <em>x &gt;= 0</em>. 
</p>
<p>Note that Abramowitz &amp; Stegun call <em>P(a,x)</em> the incomplete gamma
function (section 6.5).
</p></dd></dl>




</body>
</html>