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
|
<html lang="en">
<head>
<title>Complex Hyperbolic Functions - 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 4.8">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Complex-Numbers.html" title="Complex Numbers">
<link rel="prev" href="Inverse-Complex-Trigonometric-Functions.html" title="Inverse Complex Trigonometric Functions">
<link rel="next" href="Inverse-Complex-Hyperbolic-Functions.html" title="Inverse Complex Hyperbolic 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 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 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 freedom to copy and modify this
GNU Manual, like GNU software.''-->
<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="Complex-Hyperbolic-Functions"></a>
Next: <a rel="next" accesskey="n" href="Inverse-Complex-Hyperbolic-Functions.html">Inverse Complex Hyperbolic Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Inverse-Complex-Trigonometric-Functions.html">Inverse Complex Trigonometric Functions</a>,
Up: <a rel="up" accesskey="u" href="Complex-Numbers.html">Complex Numbers</a>
<hr>
</div>
<h3 class="section">5.7 Complex Hyperbolic Functions</h3>
<p><a name="index-hyperbolic-functions_002c-complex-numbers-203"></a>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_sinh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fsinh-204"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic sine of the complex number
<var>z</var>, \sinh(z) = (\exp(z) - \exp(-z))/2.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_cosh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcosh-205"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic cosine of the complex number
<var>z</var>, \cosh(z) = (\exp(z) + \exp(-z))/2.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_tanh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005ftanh-206"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic tangent of the complex number
<var>z</var>, \tanh(z) = \sinh(z)/\cosh(z).
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_sech</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fsech-207"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic secant of the complex
number <var>z</var>, \sech(z) = 1/\cosh(z).
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_csch</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcsch-208"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic cosecant of the complex
number <var>z</var>, \csch(z) = 1/\sinh(z).
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_coth</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcoth-209"></a></var><br>
<blockquote><p>This function returns the complex hyperbolic cotangent of the complex
number <var>z</var>, \coth(z) = 1/\tanh(z).
</p></blockquote></div>
<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>
|
