From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fccosh.html | 71 ++++++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fccosh.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fccosh.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fccosh.html b/devdocs/c/numeric%2Fcomplex%2Fccosh.html new file mode 100644 index 00000000..5c6efd4b --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fccosh.html @@ -0,0 +1,71 @@ +

ccoshf, ccosh, ccoshl

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). 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.

Parameters

+ +
z - complex argument

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,

+

where cis(y) is cos(y) + i sin(y)

+

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

+

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)

References

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 (\({\small\cosh{x} }\)cosh(x))
(function)
C++ documentation for cosh
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/complex/ccosh +

+
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