catanh(3) BSD Library Functions Manual catanh(3)
NAME
catanh -- complex inverse hyperbolic tangent function
SYNOPSIS
double complex
catanh(double complex z);
long double complex
catanhl(long double complex z);
float complex
catanhf(float complex z);
DESCRIPTION
catanh(z) computes the inverse hyperbolic tangent of the complex float-
ing-point number z, with branch cuts outside the interval [-1, 1] along
the real axis.
catanh() returns values in a strip of the complex plane with imaginary
part in the interval [-Pi/2, Pi/2].
For all complex floating point numbers z,
catanh(conj(z)) = conj(catanh(z)).
catanh(-z) = -catanh(z)
SPECIAL VALUES
The symmetries of catanh() are used to abbreviate the specification of
special values.
catanh(0 + 0i) returns 0 + 0 i.
catanh(0 + NaN i) returns 0 + NaN i.
catanh(1 + 0i) returns inf + 0i and raises the divide-by-zero flag.
catanh(x + inf i) returns 0 + Pi/2 i, for finite positive-signed x.
catanh(x + NaN i) returns NaN + NaN i, for non-zero finite x.
catanh(inf + yi) returns 0 + Pi/2 i, for finite positive-signed y.
catanh(inf + inf i) returns 0 + Pi/2 i.
catanh(inf + NaN i) returns 0 + NaN i.
catanh(NaN + yi) returns NaN + NaN i, for finite y.
catanh(NaN + inf i) returns 0 + Pi/2 i.
catanh(NaN + NaN i) returns NaN + NaN i.
NOTES
SEE ALSO
ctanh(3) complex(3)
STANDARDS
The catanh() function conforms to ISO/IEC 9899:2011.
4th Berkeley Distribution December 11, 2006 4th Berkeley Distribution
Mac OS X 10.9.1 - Generated Tue Jan 7 07:35:03 CST 2014