| Types and the imaginary constant | |||||||||||||||||||||||||||||||
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| Manipulation | |||||||||||||||||||||||||||||||
| Power and exponential functions | |||||||||||||||||||||||||||||||
| Trigonometric functions | |||||||||||||||||||||||||||||||
| Hyperbolic functions | |||||||||||||||||||||||||||||||
Defined in header <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
Defined in header <tgmath.h> | ||
#define sinh( z ) | (4) | (since C99) |
z.z has typelongdoublecomplex,csinhl is called. ifz has typedoublecomplex,csinh is called, ifz has typefloatcomplex,csinhf is called. Ifz is real or integer, then the macro invokes the corresponding real function (sinhf,sinh,sinhl). Ifz is imaginary, then the macro invokes the corresponding real version of the functionsin, implementing the formulasinh(iy) = i sin(y), and the return type is imaginary.Contents |
| z | - | complex argument |
If no errors occur, complex hyperbolic sine ofz is returned
Errors are reported consistent withmath_errhandling
If the implementation supports IEEE floating-point arithmetic,
z is+0+0i, the result is+0+0iz is+0+∞i, the result is±0+NaNi (the sign of the real part is unspecified) andFE_INVALID is raisedz is+0+NaNi, the result is±0+NaNiz isx+∞i (for any positive finite x), the result isNaN+NaNi andFE_INVALID is raisedz isx+NaNi (for any positive finite x), the result isNaN+NaNi andFE_INVALID may be raisedz is+∞+0i, the result is+∞+0iz is+∞+yi (for any positive finite y), the result is+∞cis(y)z is+∞+∞i, the result is±∞+NaNi (the sign of the real part is unspecified) andFE_INVALID is raisedz is+∞+NaNi, the result is±∞+NaNi (the sign of the real part is unspecified)z isNaN+0i, the result isNaN+0iz isNaN+yi (for any finite nonzero y), the result isNaN+NaNi andFE_INVALID may be raisedz isNaN+NaNi, the result isNaN+NaNiwherecis(y) iscos(y) + i sin(y)
| 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
#include <stdio.h>#include <math.h>#include <complex.h> int main(void){doublecomplex z= csinh(1);// behaves like real sinh along the real lineprintf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n",creal(z),cimag(z),sinh(1)); doublecomplex z2= csinh(I);// behaves like sine along the imaginary lineprintf("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)
(C99)(C99)(C99) | computes the complex hyperbolic cosine (function)[edit] |
(C99)(C99)(C99) | computes the complex hyperbolic tangent (function)[edit] |
(C99)(C99)(C99) | computes the complex arc hyperbolic sine (function)[edit] |
(C99)(C99) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)[edit] |
C++ documentation forsinh | |
