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
|
<!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 – Reference Manual: Complex Hyperbolic Functions</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Complex Hyperbolic Functions">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Complex Hyperbolic 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="Complex-Numbers.html#Complex-Numbers" rel="up" title="Complex Numbers">
<link href="Inverse-Complex-Hyperbolic-Functions.html#Inverse-Complex-Hyperbolic-Functions" rel="next" title="Inverse Complex Hyperbolic Functions">
<link href="Inverse-Complex-Trigonometric-Functions.html#Inverse-Complex-Trigonometric-Functions" rel="previous" title="Inverse Complex Trigonometric 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="Complex-Hyperbolic-Functions"></a>
<div class="header">
<p>
Next: <a href="Inverse-Complex-Hyperbolic-Functions.html#Inverse-Complex-Hyperbolic-Functions" accesskey="n" rel="next">Inverse Complex Hyperbolic Functions</a>, Previous: <a href="Inverse-Complex-Trigonometric-Functions.html#Inverse-Complex-Trigonometric-Functions" accesskey="p" rel="previous">Inverse Complex Trigonometric Functions</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Complex-Hyperbolic-Functions-1"></a>
<h3 class="section">5.7 Complex Hyperbolic Functions</h3>
<a name="index-hyperbolic-functions_002c-complex-numbers"></a>
<dl>
<dt><a name="index-gsl_005fcomplex_005fsinh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sinh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic sine of the complex number
<var>z</var>, <em>\sinh(z) = (\exp(z) - \exp(-z))/2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcosh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_cosh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cosine of the complex number
<var>z</var>, <em>\cosh(z) = (\exp(z) + \exp(-z))/2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005ftanh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_tanh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic tangent of the complex number
<var>z</var>, <em>\tanh(z) = \sinh(z)/\cosh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fsech"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sech</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic secant of the complex
number <var>z</var>, <em>\sech(z) = 1/\cosh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcsch"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_csch</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cosecant of the complex
number <var>z</var>, <em>\csch(z) = 1/\sinh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcoth"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_coth</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cotangent of the complex
number <var>z</var>, <em>\coth(z) = 1/\tanh(z)</em>.
</p></dd></dl>
</body>
</html>
|
