File: Riemann-Zeta-Function.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 (98 lines) | stat: -rw-r--r-- 4,611 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
<!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: Riemann Zeta Function</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Riemann Zeta Function">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Riemann Zeta Function">
<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="Zeta-Functions.html#Zeta-Functions" rel="up" title="Zeta Functions">
<link href="Riemann-Zeta-Function-Minus-One.html#Riemann-Zeta-Function-Minus-One" rel="next" title="Riemann Zeta Function Minus One">
<link href="Zeta-Functions.html#Zeta-Functions" rel="previous" title="Zeta 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="Riemann-Zeta-Function"></a>
<div class="header">
<p>
Next: <a href="Riemann-Zeta-Function-Minus-One.html#Riemann-Zeta-Function-Minus-One" accesskey="n" rel="next">Riemann Zeta Function Minus One</a>, Up: <a href="Zeta-Functions.html#Zeta-Functions" accesskey="u" rel="up">Zeta Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Riemann-Zeta-Function-1"></a>
<h4 class="subsection">7.32.1 Riemann Zeta Function</h4>
<a name="index-Riemann-Zeta-Function"></a>

<p>The Riemann zeta function is defined by the infinite sum 
<em>\zeta(s) = \sum_{k=1}^\infty k^{-s}</em>.  
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fzeta_005fint"></a>Function: <em>double</em> <strong>gsl_sf_zeta_int</strong> <em>(int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fzeta_005fint_005fe"></a>Function: <em>int</em> <strong>gsl_sf_zeta_int_e</strong> <em>(int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Riemann zeta function <em>\zeta(n)</em> 
for integer <var>n</var>,
<em>n \ne 1</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fzeta"></a>Function: <em>double</em> <strong>gsl_sf_zeta</strong> <em>(double <var>s</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fzeta_005fe"></a>Function: <em>int</em> <strong>gsl_sf_zeta_e</strong> <em>(double <var>s</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Riemann zeta function <em>\zeta(s)</em>
for arbitrary <var>s</var>,
<em>s \ne 1</em>.
</p></dd></dl>





</body>
</html>