3
<title>Eta Function - GNU Scientific Library -- Reference Manual</title>
4
<meta http-equiv="Content-Type" content="text/html">
5
<meta name="description" content="GNU Scientific Library -- Reference Manual">
6
<meta name="generator" content="makeinfo 4.8">
7
<link title="Top" rel="start" href="index.html#Top">
8
<link rel="up" href="Zeta-Functions.html#Zeta-Functions" title="Zeta Functions">
9
<link rel="prev" href="Hurwitz-Zeta-Function.html#Hurwitz-Zeta-Function" title="Hurwitz Zeta Function">
10
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
12
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 The GSL Team.
14
Permission is granted to copy, distribute and/or modify this document
15
under the terms of the GNU Free Documentation License, Version 1.2 or
16
any later version published by the Free Software Foundation; with the
17
Invariant Sections being ``GNU General Public License'' and ``Free Software
18
Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
19
and with the Back-Cover Text being (a) (see below). A copy of the
20
license is included in the section entitled ``GNU Free Documentation
23
(a) The Back-Cover Text is: ``You have freedom to copy and modify this
24
GNU Manual, like GNU software.''-->
25
<meta http-equiv="Content-Style-Type" content="text/css">
26
<style type="text/css"><!--
27
pre.display { font-family:inherit }
28
pre.format { font-family:inherit }
29
pre.smalldisplay { font-family:inherit; font-size:smaller }
30
pre.smallformat { font-family:inherit; font-size:smaller }
31
pre.smallexample { font-size:smaller }
32
pre.smalllisp { font-size:smaller }
33
span.sc { font-variant:small-caps }
34
span.roman { font-family:serif; font-weight:normal; }
35
span.sansserif { font-family:sans-serif; font-weight:normal; }
41
<a name="Eta-Function"></a>
42
Previous: <a rel="previous" accesskey="p" href="Hurwitz-Zeta-Function.html#Hurwitz-Zeta-Function">Hurwitz Zeta Function</a>,
43
Up: <a rel="up" accesskey="u" href="Zeta-Functions.html#Zeta-Functions">Zeta Functions</a>
47
<h4 class="subsection">7.31.4 Eta Function</h4>
49
<p>The eta function is defined by
50
<!-- {$\eta(s) = (1-2^{1-s}) \zeta(s)$} -->
51
\eta(s) = (1-2^{1-s}) \zeta(s).
54
— Function: double <b>gsl_sf_eta_int</b> (<var>int n</var>)<var><a name="index-gsl_005fsf_005feta_005fint-808"></a></var><br>
55
— Function: int <b>gsl_sf_eta_int_e</b> (<var>int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005feta_005fint_005fe-809"></a></var><br>
56
<blockquote><p>These routines compute the eta function \eta(n) for integer <var>n</var>.
57
<!-- Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW -->
58
</p></blockquote></div>
61
— Function: double <b>gsl_sf_eta</b> (<var>double s</var>)<var><a name="index-gsl_005fsf_005feta-810"></a></var><br>
62
— Function: int <b>gsl_sf_eta_e</b> (<var>double s, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005feta_005fe-811"></a></var><br>
63
<blockquote><p>These routines compute the eta function \eta(s) for arbitrary <var>s</var>.
64
<!-- Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW -->
65
</p></blockquote></div>