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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CSINH 3
5.Os BSD 4
6.Sh NAME
7.Nm csinh
8.Nd complex hyperbolic sine function
9.Sh SYNOPSIS
10.Fd #include <complex.h>
11.Ft double complex
12.Fn csinh "double complex z"
13.Ft long double complex
14.Fn csinhl "long double complex z"
15.Ft float complex
16.Fn csinhf "float complex z"
17.Sh DESCRIPTION
18.Fn csin "z"
19computes the hyperbolic sine of the complex floating-point number
20.Fa z .
21.Pp
22For all complex floating point numbers z,
23.Bd -literal -offset indent
24csinh(conj(z)) = conj(csinh(z)),
25.br
26csinh(-z) = -csinh(z).
27.Ed
28.Sh SPECIAL VALUES
29The symmetries of csinh() are used to abbreviate the specification of special values.
30.Pp
31.Fn csinh "0 + 0i"
32returns 0 + 0i.
33.Pp
34.Fn csinh "0 + inf i"
35returns 0 + NaN i, and raises the invalid flag.
36.Pp
37.Fn csinh "0 + NaN i"
38returns 0 + NaN i.
39.Pp
40.Fn csinh "x + inf i"
41returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.
42.Pp
43.Fn csinh "x + NaN i"
44returns NaN + NaN i, for finite nonzero x.
45.Pp
46.Fn csinh "inf + 0i"
47returns inf + 0i.
48.Pp
49.Fn csinh "inf + yi"
50returns inf * cis(y), for finite positive y, where cis(y) = cos(y) + i*sin(y).
51.Pp
52.Fn csinh "inf + inf i"
53returns inf + NaN i, and raises the invalid flag.
54.Pp
55.Fn csinh "inf + NaN i"
56returns inf + NaN i.
57.Pp
58.Fn csinh "NaN + 0i"
59returns NaN + 0i.
60.Pp
61.Fn csinh "NaN + yi"
62returns NaN + NaN i, for nonzero numbers y.
63.Pp
64.Fn csinh "NaN + NaN i"
65returns NaN + NaN i.
66.Sh NOTES
67.Sh SEE ALSO
68.Xr csin 3
69.Xr complex 3
70.Sh STANDARDS
71The
72.Fn csinh
73function conforms to ISO/IEC 9899:1999(E).