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
|
<html lang="en">
<head>
<title>Psi (Digamma) Function - 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 4.11">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Special-Functions.html" title="Special Functions">
<link rel="prev" href="Power-Function.html" title="Power Function">
<link rel="next" href="Synchrotron-Functions.html" title="Synchrotron 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, 2008, 2009, 2010 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.''-->
<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="Psi-(Digamma)-Function"></a>
<a name="Psi-_0028Digamma_0029-Function"></a>
Next: <a rel="next" accesskey="n" href="Synchrotron-Functions.html">Synchrotron Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Power-Function.html">Power Function</a>,
Up: <a rel="up" accesskey="u" href="Special-Functions.html">Special Functions</a>
<hr>
</div>
<h3 class="section">7.28 Psi (Digamma) Function</h3>
<p><a name="index-psi-function-782"></a><a name="index-digamma-function-783"></a><a name="index-polygamma-functions-784"></a>
The polygamma functions of order n are defined by
<pre class="example"> \psi^{(n)}(x) = (d/dx)^n \psi(x) = (d/dx)^{n+1} \log(\Gamma(x))
</pre>
<p class="noindent">where \psi(x) = \Gamma'(x)/\Gamma(x) is known as the digamma function.
These functions are declared in the header file <samp><span class="file">gsl_sf_psi.h</span></samp>.
<ul class="menu">
<li><a accesskey="1" href="Digamma-Function.html">Digamma Function</a>
<li><a accesskey="2" href="Trigamma-Function.html">Trigamma Function</a>
<li><a accesskey="3" href="Polygamma-Function.html">Polygamma Function</a>
</ul>
<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>
|
