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ccoshf, ccosh, ccoshl

From cppreference.com
< c‎ | numeric‎ | complex
Defined in header <complex.h>
float complex       ccoshf( float complex z );
(1) (since C99)
double complex      ccosh( double complex z );
(2) (since C99)
long double complex ccoshl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define cosh( z )
(4) (since C99)
1-3) Computes the complex hyperbolic cosine of z.
4) Type-generic macro: If z has type long double complex, ccoshl is called. if z has type double complex, ccosh is called, if z has type float complex, ccoshf is called. If z is real or integer, then the macro invokes the corresponding real function (coshf, cosh, coshl)

Contents

[edit] Parameters

z - complex argument

[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

Mathematical definition of hyperbolic cosine is cosh z =
ez
+e-z
2

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));
}

Output:

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

[edit] See also

(C99)(C99)(C99)
computes the complex hyperbolic sine
(function) [edit]
(C99)(C99)(C99)
computes the complex hyperbolic tangent
(function) [edit]
(C99)(C99)(C99)
computes the complex arc hyperbolic cosine
(function) [edit]
(C99)(C99)
computes hyperbolic cosine (ch(x))
(function) [edit]