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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CASINH 3
5.Os BSD 4
6.Sh NAME
7.Nm casinh
8.Nd complex inverse hyperbolic sine function
9.Sh SYNOPSIS
10.Ft double complex
11.Fn casinh "double complex z"
12.Ft long double complex
13.Fn casinhl "long double complex z"
14.Ft float complex
15.Fn casinhf "float complex z"
16.Sh DESCRIPTION
17.Fn casinh "z"
18computes the inverse hyperbolic sine of the complex floating-point number
19.Fa z ,
20with branch cuts outside the interval
21.Bq -i, i
22along the imaginary axis.
23.Pp
24.Fn casinh
25returns values in a strip of the complex plane with imaginary part in the interval
26.Bq -Pi/2 , Pi/2 .
27.Pp
28For all complex floating point numbers z,
29.Bd -literal -offset indent
30casinh(conj(z)) = conj(casinh(z)).
31casinh(-z) = -casinh(z)
32.Ed
33.Sh SPECIAL VALUES
34The symmetries of casinh() are used to abbreviate the specification of special values.
35.Pp
36.Fn casinh "0 + 0i"
37returns 0 + 0 i.
38.Pp
39.Fn casinh "x + inf i"
40returns inf + Pi/2 i, for finite positive-signed x.
41.Pp
42.Fn casinh "x + NaN i"
43returns NaN + NaN i, for finite x.
44.Pp
45.Fn casinh "inf + yi"
46returns inf + 0i, for finite positive-signed y.
47.Pp
48.Fn casinh "inf + inf i"
49returns inf + Pi/4 i.
50.Pp
51.Fn casinh "inf + NaN i"
52returns inf + NaN i.
53.Pp
54.Fn casinh "NaN + 0i"
55returns NaN + 0i.
56.Pp
57.Fn casinh "NaN + yi"
58returns NaN + NaN i, for finite y.
59.Pp
60.Fn casinh "NaN + inf i"
61returns inf + NaN i.
62.Pp
63.Fn casinh "NaN + NaN i"
64returns NaN + NaN i.
65.Sh NOTES
66.Sh SEE ALSO
67.Xr csinh 3
68.Xr complex 3
69.Sh STANDARDS
70The
71.Fn casinh
72function conforms to ISO/IEC 9899:1999(E).