015j_casinh.asciidoc

casinh

NAME

casinh - complex arc hyperbolic sine

SYNOPSIS

#include <complex.h>

double complex      casinh  (double complex z);
float complex       casinhf (float complex z);
long double complex casinhl (long double complex z);

CONFORMING TO

C99

DESCRIPTION

The casinh() function calculates the complex arc hyperbolic sine of z. If y = casinh(z), then z = csinh(y). The imaginary part of y is chosen in the interval [-pi/2,pi/2].

One has: casinh(z) = clog(z + csqrt(z * z + 1))

RETURN VALUE

Returns the complex arc hyperbolic sine value in the range of a strip mathematically unbound along the real axis in the interval [-I*pi,I*pi] along the imaginary axis.

SEE ALSO

asinh, cabs, csinh, cimag, complex

EXAMPLE

link:src/casinh.c[role=include]

OUTPUT

$ gcc -Wall -lm casinh.c
$ ./a.out
casinh(+0+2i) = 1.316958+1.570796i
casinh(-0+2i) (the other side of the cut) = -1.316958+1.570796i
casinh(1+2i) = 1.469352+1.063440i
casin(i * (1+2i))/i = 1.469352+1.063440i