# ctanh.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CTANH 3
.Os BSD 4
.Sh NAME
.Nm ctanh
.Nd complex hyperbolic tangent function
.Sh SYNOPSIS
.Ft double complex
.Fn ctanh "double complex z"
.Ft long double complex
.Fn ctanhl "long double complex z"
.Ft float complex
.Fn ctanhf "float complex z"
.Sh DESCRIPTION
.Fn ctanh "z"
computes the hyperbolic tangent of the complex floating-point number
.Fa z .
.Pp
For all complex floating point numbers z,
.Bd -literal -offset indent
ctanh(conj(z)) = conj(ctanh(z)),
.br
ctanh(-z) = -ctanh(z).
.Ed
.Sh SPECIAL VALUES
The symmetries of ctanh() are used to abbreviate the specification of special values.
.Pp
.Fn ctanh "0 + 0i"
returns 0 + 0i.
.Pp
.Fn ctanh "0 + inf i"
returns NaN + NaN i, and raises the invalid flag.
.Pp
.Fn ctanh "0 + NaN i"
returns NaN + NaN i.
.Pp
.Fn ctanh "x + inf i"
returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.
.Pp
.Fn ctanh "x + NaN i"
returns NaN + NaN i, for finite nonzero x.
.Pp
.Fn ctanh "inf + 0i"
returns 1 + 0i.
.Pp
.Fn ctanh "inf + yi"
returns 1 ± 0i, for finite positive y, with the sign chosen to match the sign of sin(2y).
.Pp
.Fn ctanh "inf + inf i"
returns 1 + 0i.
.Pp
.Fn ctanh "inf + NaN i"
returns 1 + 0i.
.Pp
.Fn ctanh "NaN + 0i"
returns NaN + 0i.
.Pp
.Fn ctanh "NaN + yi"
returns NaN + NaN i, for nonzero numbers y.
.Pp
.Fn ctanh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES
.Sh SEE ALSO
.Xr ctan 3
.Xr complex 3
.Sh STANDARDS
The
.Fn ctanh
function conforms to ISO/IEC 9899:1999(E).```