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 9899:2011.