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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CCOSH 3
5.Os BSD 4
6.Sh NAME
7.Nm ccosh
8.Nd complex hyperbolic cosine function
9.Sh SYNOPSIS
10.Ft double complex
11.Fn ccosh "double complex z"
12.Ft long double complex
13.Fn ccoshl "long double complex z"
14.Ft float complex
15.Fn ccoshf "float complex z"
16.Sh DESCRIPTION
17.Fn ccos "z"
18computes the hyperbolic cosine of the complex floating-point number
19.Fa z .
20.Pp
21For all complex floating point numbers z,
22.Bd -literal -offset indent
23ccosh(conj(z)) = conj(ccosh(z)),
24.br
25ccosh(-z) = ccosh(z).
26.Ed
27.Sh SPECIAL VALUES
28The symmetries of ccosh() are used to abbreviate the specification of special values.
29.Pp
30.Fn ccosh "0 + 0i"
31returns 1 + 0i.
32.Pp
33.Fn ccosh "0 + inf i"
34returns NaN + 0i, and raises the invalid flag.
35.Pp
36.Fn ccosh "0 + NaN i"
37returns NaN + 0i.
38.Pp
39.Fn ccosh "x + inf i"
40returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.
41.Pp
42.Fn ccosh "x + NaN i"
43returns NaN + NaN i, for finite nonzero x.
44.Pp
45.Fn ccosh "inf + 0i"
46returns inf + 0i.
47.Pp
48.Fn ccosh "inf + yi"
49returns inf * cis(y), for finite positive y, where cis(y) = cos(y) + i*sin(y).
50.Pp
51.Fn ccosh "inf + inf i"
52returns inf + NaN i, and raises the invalid flag.
53.Pp
54.Fn ccosh "inf + NaN i"
55returns inf + NaN i.
56.Pp
57.Fn ccosh "NaN + 0i"
58returns NaN + 0i.
59.Pp
60.Fn ccosh "NaN + yi"
61returns NaN + NaN i, for nonzero numbers y.
62.Pp
63.Fn ccosh "NaN + NaN i"
64returns NaN + NaN i.
65.Sh NOTES
66.Sh SEE ALSO
67.Xr ccos 3
68.Xr complex 3
69.Sh STANDARDS
70The
71.Fn ccosh
72function conforms to ISO/IEC 9899:1999(E).