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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(_ + _i) 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 + _i) 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                     December 11, 2006                    4th Berkeley Distribution