CASINH(3)                BSD Library Functions Manual                CASINH(3)

NAME
     casinh -- complex inverse hyperbolic sine function

SYNOPSIS
     double complex
     casinh(double complex z);

     long double complex
     casinhl(long double complex z);

     float complex
     casinhf(float complex z);

DESCRIPTION
     casinh(z) computes the inverse hyperbolic sine of the complex floating-
     point number z, with branch cuts outside the interval [-i, i] along the
     imaginary axis.

     casinh() 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,

           casinh(conj(z)) = conj(casinh(z)).
           casinh(-z) = -casinh(z)

SPECIAL VALUES
     The symmetries of casinh() are used to abbreviate the specification of
     special values.

     casinh(0 ] 0i) returns 0 ] 0 i.

     casinh(x ] inf i) returns inf ] Pi/2 i, for finite positive-signed x.

     casinh(x ] NaN i) returns NaN ] NaN i, for finite x.

     casinh(inf ] yi) returns inf ] 0i, for finite positive-signed y.

     casinh(inf ] inf i) returns inf ] Pi/4 i.

     casinh(inf ] NaN i) returns inf ] NaN i.

     casinh(NaN ] 0i) returns NaN ] 0i.

     casinh(NaN ] yi) returns NaN ] NaN i, for finite y.

     casinh(NaN ] inf i) returns inf ] NaN i.

     casinh(NaN ] NaN i) returns NaN ] NaN i.

NOTES
SEE ALSO
     csinh(3) complex(3)

STANDARDS
     The casinh() function conforms to ISO/IEC 9899:1999(E).

4th Berkeley Distribution      November 9, 2006      4th Berkeley Distribution