ccoshf, ccosh, ccoshl

float complex       ccoshf( float complex z );

double complex      ccosh( double complex z );

long double complex ccoshl( long double complex z );

#define cosh( z )

Parameters

Return value

If no errors occur, complex hyperbolic cosine of z is returned.

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• ccosh(conj(z)) == conj(ccosh(z))
• ccosh(z) == ccosh(-z)
• If z is +0+0i, the result is 1+0i
• If z is +0+∞i, the result is NaN±0i (the sign of the imaginary part is unspecified) and FE_INVALID is raised
• If z is +0+NaNi, the result is NaN±0i (the sign of the imaginary part is unspecified)
• If z is x+∞i (for any finite non-zero x), the result is NaN+NaNi and FE_INVALID is raised
• If z is x+NaNi (for any finite non-zero 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 finite non-zero 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 +∞+NaN, the result is +∞+NaN
• If z is NaN+0i, the result is NaN±0i (the sign of the imaginary part is unspecified)
• If z is NaN+yi (for any finite non-zero 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 cosine 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 = ccosh(1);  // behaves like real cosh along the real line
    printf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n", creal(z), cimag(z), cosh(1));
 
    double complex z2 = ccosh(I); // behaves like real cosine along the imaginary line
    printf("cosh(0+1i) = %f%+fi ( cos(1)=%f)\n", creal(z2), cimag(z2), cos(1));
}

cosh(1+0i) = 1.543081+0.000000i (cosh(1)=1.543081)
cosh(0+1i) = 0.540302+0.000000i ( cos(1)=0.540302)

References

• C11 standard (ISO/IEC 9899:2011):
• 7.3.6.4 The ccosh functions (p: 193)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.2.4 The ccosh functions (p: 541)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.6.4 The ccosh functions (p: 175)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.2.4 The ccosh functions (p: 476)
• G.7 Type-generic math <tgmath.h> (p: 480)

See also