NAME

csinh — complex hyperbolic sine function

SYNOPSIS

double complex
csinh(double complex z);

long double complex
csinhl(long double complex z);

float complex
csinhf(float complex z);

csin(z) computes the hyperbolic sine of the complex floating-point number z.

For all complex floating point numbers z,

csinh(conj(z)) = conj(csinh(z)),
csinh(-z) = -csinh(z).

The symmetries of csinh() are used to abbreviate the specification of special values.

csinh(0 + 0i) returns 0 + 0i.

csinh(0 + inf i) returns 0 + NaN i, and raises the invalid flag.

csinh(0 + NaN i) returns 0 + NaN i.

csinh(x + inf i) returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.

csinh(x + NaN i) returns NaN + NaN i, for finite nonzero x.

csinh(inf + 0i) returns inf + 0i.

csinh(inf + yi) returns inf * cis(y), for finite positive y, where cis(y) = cos(y) + i*sin(y).

csinh(inf + inf i) returns inf + NaN i, and raises the invalid flag.

csinh(inf + NaN i) returns inf + NaN i.

csinh(NaN + 0i) returns NaN + 0i.

csinh(NaN + yi) returns NaN + NaN i, for nonzero numbers y.

csinh(NaN + NaN i) returns NaN + NaN i.

The csinh() function conforms to ISO/IEC 9899:2011.