# ccosh.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd November 9, 2006
.Dt CCOSH 3
.Os BSD 4
.Sh NAME
.Nm ccosh
.Nd complex hyperbolic cosine function
.Sh SYNOPSIS
.Ft double complex
.Fn ccosh "double complex z"
.Ft long double complex
.Fn ccoshl "long double complex z"
.Ft float complex
.Fn ccoshf "float complex z"
.Sh DESCRIPTION
.Fn ccos "z"
computes the hyperbolic cosine of the complex floating-point number
.Fa z .
.Pp
For all complex floating point numbers z,
.Bd -literal -offset indent
ccosh(conj(z)) = conj(ccosh(z)),
.br
ccosh(-z) = ccosh(z).
.Ed
.Sh SPECIAL VALUES
The symmetries of ccosh() are used to abbreviate the specification of special values.
.Pp
.Fn ccosh "0 + 0i"
returns 1 + 0i.
.Pp
.Fn ccosh "0 + inf i"
returns NaN + 0i, and raises the invalid flag.
.Pp
.Fn ccosh "0 + NaN i"
returns NaN + 0i.
.Pp
.Fn ccosh "x + inf i"
returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.
.Pp
.Fn ccosh "x + NaN i"
returns NaN + NaN i, for finite nonzero x.
.Pp
.Fn ccosh "inf + 0i"
returns inf + 0i.
.Pp
.Fn ccosh "inf + yi"
returns inf * cis(y), for finite positive y, where cis(y) = cos(y) + i*sin(y).
.Pp
.Fn ccosh "inf + inf i"
returns inf + NaN i, and raises the invalid flag.
.Pp
.Fn ccosh "inf + NaN i"
returns inf + NaN i.
.Pp
.Fn ccosh "NaN + 0i"
returns NaN + 0i.
.Pp
.Fn ccosh "NaN + yi"
returns NaN + NaN i, for nonzero numbers y.
.Pp
.Fn ccosh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES