ccoshf, ccosh, ccoshl
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                    | Defined in header  <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (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). If z is imaginary, then the macro invokes the corresponding real version of the function cos, implementing the formula cosh(iy) = cos(y), and the return type is real.| 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 zis+0+0i, the result is1+0i
-  If zis+0+∞i, the result isNaN±0i(the sign of the imaginary part is unspecified) and FE_INVALID is raised
-  If zis+0+NaNi, the result isNaN±0i(the sign of the imaginary part is unspecified)
-  If zisx+∞i(for any finite non-zero x), the result isNaN+NaNiand FE_INVALID is raised
-  If zisx+NaNi(for any finite non-zero x), the result isNaN+NaNiand FE_INVALID may be raised
-  If zis+∞+0i, the result is+∞+0i
-  If zis+∞+yi(for any finite non-zero y), the result is+∞+cis(y)
-  If zis+∞+∞i, the result is±∞+NaNi(the sign of the real part is unspecified) and FE_INVALID is raised
-  If zis+∞+NaN, the result is+∞+NaN
-  If zisNaN+0i, the result isNaN±0i(the sign of the imaginary part is unspecified)
-  If zisNaN+yi(for any finite non-zero y), the result isNaN+NaNiand FE_INVALID may be raised
-  If zisNaN+NaNi, the result isNaN+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
Run this code
#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] 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)
 
[edit] See also
| (C99)(C99)(C99) | computes the complex hyperbolic sine (function) | 
| (C99)(C99)(C99) | computes the complex hyperbolic tangent (function) | 
| (C99)(C99)(C99) | computes the complex arc hyperbolic cosine (function) | 
| (C99)(C99) | computes hyperbolic cosine (ch(x)) (function) | 
| C++ documentation for cosh | |


