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csinhf, csinh, csinhl

Defined in header <complex.h> 
float complex       csinhf( float complex z );
-		 (1) (since C99) 
double complex      csinh( double complex z );
-		 (2) (since C99) 
long double complex csinhl( long double complex z );
-		 (3) (since C99)
Defined in header <tgmath.h> 
#define sinh( z )
-		 (4) (since C99)
-1-3) Computes the complex hyperbolic sine of z.
-4) Type-generic macro: If z has type long double complex, csinhl is called. if z has type double complex, csinh is called, if z has type float complex, csinhf is called. If z is real or integer, then the macro invokes the corresponding real function (sinhf, sinh, sinhl). If z is imaginary, then the macro invokes the corresponding real version of the function sin, implementing the formula sinh(iy) = i sin(y), and the return type is imaginary.

Parameters

- -
z - complex argument

Return value

If no errors occur, complex hyperbolic sine 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 sine is sinh z = ez-e-z/2

Hyperbolic sine 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 = csinh(1);  // behaves like real sinh along the real line
-    printf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n", creal(z), cimag(z), sinh(1));
- 
-    double complex z2 = csinh(I); // behaves like sine along the imaginary line
-    printf("sinh(0+1i) = %f%+fi ( sin(1)=%f)\n", creal(z2), cimag(z2), sin(1));
-}

Output:

-
sinh(1+0i) = 1.175201+0.000000i (sinh(1)=1.175201)
-sinh(0+1i) = 0.000000+0.841471i ( sin(1)=0.841471)

References

See also

- - - - -
-
(C99)(C99)(C99)
 computes the complex hyperbolic cosine
(function)
-
(C99)(C99)(C99)
 computes the complex hyperbolic tangent
(function)
-
(C99)(C99)(C99)
 computes the complex arc hyperbolic sine
(function)
-
(C99)(C99)
 computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x))
(function)
C++ documentation for sinh
-

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

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