# catanh.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CATANH 3
.Os BSD 4
.Sh NAME
.Nm catanh
.Nd complex inverse hyperbolic tangent function
.Sh SYNOPSIS
.Ft double complex
.Fn catanh "double complex z"
.Ft long double complex
.Fn catanhl "long double complex z"
.Ft float complex
.Fn catanhf "float complex z"
.Sh DESCRIPTION
.Fn catanh "z"
computes the inverse hyperbolic tangent of the complex floating-point number
.Fa z ,
with branch cuts outside the interval
.Bq -1, 1
along the real axis.
.Pp
.Fn catanh
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
catanh(conj(z)) = conj(catanh(z)).
catanh(-z) = -catanh(z)
.Ed
.Sh SPECIAL VALUES
The symmetries of catanh() are used to abbreviate the specification of special values.
.Pp
.Fn catanh "0 + 0i"
returns 0 + 0 i.
.Pp
.Fn catanh "0 + NaN i"
returns 0 + NaN i.
.Pp
.Fn catanh "1 + 0i"
returns inf + 0i and raises the divide-by-zero flag.
.Pp
.Fn catanh "x + inf i"
returns 0 + Pi/2 i, for finite positive-signed x.
.Pp
.Fn catanh "x + NaN i"
returns NaN + NaN i, for non-zero finite x.
.Pp
.Fn catanh "inf + yi"
returns 0 + Pi/2 i, for finite positive-signed y.
.Pp
.Fn catanh "inf + inf i"
returns 0 + Pi/2 i.
.Pp
.Fn catanh "inf + NaN i"
returns 0 + NaN i.
.Pp
.Fn catanh "NaN + yi"
returns NaN + NaN i, for finite y.
.Pp
.Fn catanh "NaN + inf i"
returns 0 + Pi/2 i.
.Pp
.Fn catanh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES