Computes complex hyperbolic sine of a complex valuez.

[edit]Parameters

[edit]Return value

If no errors occur, complex hyperbolic sine ofz is returned.

[edit]Error handling and special values

Errors are reported consistent withmath_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• std::sinh(std::conj(z))==std::conj(std::sinh(z))
• std::sinh(z)==-std::sinh(-z)
• Ifz is(+0,+0), the result is(+0,+0)
• Ifz is(+0,+∞), the result is(±0,NaN) (the sign of the real part is unspecified) andFE_INVALID is raised
• Ifz is(+0,NaN), the result is(±0,NaN)
• Ifz is(x,+∞) (for any positive finite x), the result is(NaN,NaN) andFE_INVALID is raised
• Ifz is(x,NaN) (for any positive finite x), the result is(NaN,NaN) andFE_INVALID may be raised
• Ifz is(+∞,+0), the result is(+∞,+0)
• Ifz is(+∞,y) (for any positive finite y), the result is+∞cis(y)
• Ifz is(+∞,+∞), the result is(±∞,NaN) (the sign of the real part is unspecified) andFE_INVALID is raised
• Ifz is(+∞,NaN), the result is(±∞,NaN) (the sign of the real part is unspecified)
• Ifz is(NaN,+0), the result is(NaN,+0)
• Ifz is(NaN,y) (for any finite nonzero y), the result is(NaN,NaN) andFE_INVALID may be raised
• Ifz is(NaN,NaN), the result is(NaN,NaN)

wherecis(y) iscos(y) + i sin(y).

[edit]Notes

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 period2πi.

[edit]Example

#include <cmath>#include <complex>#include <iostream> int main(){std::cout<<std::fixed;std::complex<double> z(1.0,0.0);// behaves like real sinh along the real linestd::cout<<"sinh"<< z<<" = "<<std::sinh(z)<<" (sinh(1) = "<<std::sinh(1)<<")\n"; std::complex<double> z2(0.0,1.0);// behaves like sine along the imaginary linestd::cout<<"sinh"<< z2<<" = "<<std::sinh(z2)<<" ( sin(1) = "<<std::sin(1)<<")\n";}

sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201)sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471)

[edit]See also

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