File: Debye-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 (130 lines) | stat: -rw-r--r-- 6,684 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
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
<!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: Debye Functions</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Debye Functions">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Debye 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="Special-Functions.html#Special-Functions" rel="up" title="Special Functions">
<link href="Dilogarithm.html#Dilogarithm" rel="next" title="Dilogarithm">
<link href="Dawson-Function.html#Dawson-Function" rel="previous" title="Dawson Function">
<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="Debye-Functions"></a>
<div class="header">
<p>
Next: <a href="Dilogarithm.html#Dilogarithm" accesskey="n" rel="next">Dilogarithm</a>, Previous: <a href="Dawson-Function.html#Dawson-Function" accesskey="p" rel="previous">Dawson Function</a>, Up: <a href="Special-Functions.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Debye-Functions-1"></a>
<h3 class="section">7.10 Debye Functions</h3>
<a name="index-Debye-functions"></a>

<p>The Debye functions <em>D_n(x)</em> are defined by the following integral,
</p>
<div class="example">
<pre class="example">D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1))
</pre></div>

<p>For further information see Abramowitz &amp;
Stegun, Section 27.1.  The Debye functions are declared in the header
file <samp>gsl_sf_debye.h</samp>.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f1"></a>Function: <em>double</em> <strong>gsl_sf_debye_1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the first-order Debye function 
<em>D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f2"></a>Function: <em>double</em> <strong>gsl_sf_debye_2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the second-order Debye function 
<em>D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f3"></a>Function: <em>double</em> <strong>gsl_sf_debye_3</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f3_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_3_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the third-order Debye function 
<em>D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f4"></a>Function: <em>double</em> <strong>gsl_sf_debye_4</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f4_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_4_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the fourth-order Debye function 
<em>D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f5"></a>Function: <em>double</em> <strong>gsl_sf_debye_5</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f5_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_5_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the fifth-order Debye function 
<em>D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f6"></a>Function: <em>double</em> <strong>gsl_sf_debye_6</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f6_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_6_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the sixth-order Debye function 
<em>D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1))</em>.
</p></dd></dl>




</body>
</html>