ccoshf, ccosh, ccoshl

[edit] Parameters

[edit] Return value

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

[edit] 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)

[edit] 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

[edit] 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)

[edit] References

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