[edit]Parameters

[edit]Return value

If no errors occur, complex hyperbolic cosine ofz is returned

[edit]Error handling and special values

Errors are reported consistent withmath_errhandling

If the implementation supports IEEE floating-point arithmetic,

• ccosh(conj(z))==conj(ccosh(z))
• ccosh(z)== ccosh(-z)
• Ifz is+0+0i, the result is1+0i
• Ifz is+0+∞i, the result isNaN±0i (the sign of the imaginary part is unspecified) andFE_INVALID is raised
• Ifz is+0+NaNi, the result isNaN±0i (the sign of the imaginary part is unspecified)
• Ifz isx+∞i (for any finite non-zero x), the result isNaN+NaNi andFE_INVALID is raised
• Ifz isx+NaNi (for any finite non-zero x), the result isNaN+NaNi andFE_INVALID may be raised
• Ifz is+∞+0i, the result is+∞+0i
• Ifz is+∞+yi (for any finite non-zero y), the result is+∞cis(y)
• Ifz is+∞+∞i, the result is±∞+NaNi (the sign of the real part is unspecified) andFE_INVALID is raised
• Ifz is+∞+NaN, the result is+∞+NaN
• Ifz isNaN+0i, the result isNaN±0i (the sign of the imaginary part is unspecified)
• Ifz isNaN+yi (for any finite non-zero y), the result isNaN+NaNi andFE_INVALID may be raised
• Ifz isNaN+NaNi, the result isNaN+NaNi

wherecis(y) iscos(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){doublecomplex z= ccosh(1);// behaves like real cosh along the real lineprintf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n",creal(z),cimag(z),cosh(1)); doublecomplex z2= ccosh(I);// behaves like real cosine along the imaginary lineprintf("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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