# casinh.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CASINH 3
.Os BSD 4
.Sh NAME
.Nm casinh
.Nd complex inverse hyperbolic sine function
.Sh SYNOPSIS
.Ft double complex
.Fn casinh "double complex z"
.Ft long double complex
.Fn casinhl "long double complex z"
.Ft float complex
.Fn casinhf "float complex z"
.Sh DESCRIPTION
.Fn casinh "z"
computes the inverse hyperbolic sine of the complex floating-point number
.Fa z ,
with branch cuts outside the interval
.Bq -i, i
along the imaginary axis.
.Pp
.Fn casinh
returns values in a strip of the complex plane with imaginary part in the interval
.Bq -Pi/2 , Pi/2 .
.Pp
For all complex floating point numbers z,
.Bd -literal -offset indent
casinh(conj(z)) = conj(casinh(z)).
casinh(-z) = -casinh(z)
.Ed
.Sh SPECIAL VALUES
The symmetries of casinh() are used to abbreviate the specification of special values.
.Pp
.Fn casinh "0 + 0i"
returns 0 + 0 i.
.Pp
.Fn casinh "x + inf i"
returns inf + Pi/2 i, for finite positive-signed x.
.Pp
.Fn casinh "x + NaN i"
returns NaN + NaN i, for finite x.
.Pp
.Fn casinh "inf + yi"
returns inf + 0i, for finite positive-signed y.
.Pp
.Fn casinh "inf + inf i"
returns inf + Pi/4 i.
.Pp
.Fn casinh "inf + NaN i"
returns inf + NaN i.
.Pp
.Fn casinh "NaN + 0i"
returns NaN + 0i.
.Pp
.Fn casinh "NaN + yi"
returns NaN + NaN i, for finite y.
.Pp
.Fn casinh "NaN + inf i"
returns inf + NaN i.
.Pp
.Fn casinh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES