csinhf, csinh, csinhl

Parameters

Return value

If no errors occur, complex hyperbolic sine of z is returned

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• csinh ( conj ( z ) ) == conj ( csinh ( z ) )
• csinh ( z ) == - csinh ( - z )
• If z is +0+0i , the result is +0+0i
• If z is +0+∞i , the result is ±0+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is +0+NaNi , the result is ±0+NaNi
• If z is x+∞i (for any positive finite x), the result is NaN+NaNi and FE_INVALID is raised
• If z is x+NaNi (for any positive finite x), the result is NaN+NaNi and FE_INVALID may be raised
• If z is +∞+0i , the result is +∞+0i
• If z is +∞+yi (for any positive finite y), the result is +∞cis(y)
• If z is +∞+∞i , the result is ±∞+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is +∞+NaNi , the result is ±∞+NaNi (the sign of the real part is unspecified)
• If z is NaN+0i , the result is NaN+0i
• If z is NaN+yi (for any finite nonzero y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+NaNi , the result is NaN+NaNi

where cis(y) is cos(y) + i sin(y)

Notes

Hyperbolic sine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi

Example

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    double complex z = csinh(1);  // behaves like real sinh along the real line
    printf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n", creal(z), cimag(z), sinh(1));
 
    double complex z2 = csinh(I); // behaves like sine along the imaginary line
    printf("sinh(0+1i) = %f%+fi ( sin(1)=%f)\n", creal(z2), cimag(z2), sin(1));
}

sinh(1+0i) = 1.175201+0.000000i (sinh(1)=1.175201)
sinh(0+1i) = 0.000000+0.841471i ( sin(1)=0.841471)

References