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Defined in header <complex> | ||
template<class T> complex<T> cosh(const complex<T>& z); | (since C++11) | |
Computes complex hyperbolic cosine of a complex valuez.
Contents |
| z | - | complex value |
If no errors occur, complex hyperbolic cosine ofz is returned.
Errors are reported consistent withmath_errhandling.
If the implementation supports IEEE floating-point arithmetic,
(+0,+0), the result is(1,+0)(+0,+∞), the result is(NaN,±0) (the sign of the imaginary part is unspecified) andFE_INVALID is raised(+0,NaN), the result is(NaN,±0) (the sign of the imaginary part is unspecified)(x,+∞) (for any finite non-zero x), the result is(NaN,NaN) andFE_INVALID is raised(x,NaN) (for any finite non-zero x), the result is(NaN,NaN) andFE_INVALID may be raised(+∞,+0), the result is(+∞,+0)(+∞,y) (for any finite non-zero y), the result is+∞cis(y)(+∞,+∞), the result is(±∞,NaN) (the sign of the real part is unspecified) andFE_INVALID is raised(+∞,NaN), the result is(+∞,NaN)(NaN,+0), the result is(NaN,±0) (the sign of the imaginary part is unspecified)(NaN,+y) (for any finite non-zero y), the result is(NaN,NaN) andFE_INVALID may be raised(NaN,NaN), the result is(NaN,NaN)wherecis(y) iscos(y) + i sin(y).
| 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.
#include <cmath>#include <complex>#include <iostream> int main(){std::cout<<std::fixed;std::complex<double> z(1.0,0.0);// behaves like real cosh along the real linestd::cout<<"cosh"<< z<<" = "<<std::cosh(z)<<" (cosh(1) = "<<std::cosh(1)<<")\n"; std::complex<double> z2(0.0,1.0);// behaves like real cosine along the imaginary linestd::cout<<"cosh"<< z2<<" = "<<std::cosh(z2)<<" ( cos(1) = "<<std::cos(1)<<")\n";}
Output:
cosh(1.000000,0.000000) = (1.543081,0.000000) (cosh(1) = 1.543081)cosh(0.000000,1.000000) = (0.540302,0.000000) ( cos(1) = 0.540302)
| computes hyperbolic sine of a complex number (\({\small\sinh{z}}\)sinh(z)) (function template)[edit] | |
| computes hyperbolic tangent of a complex number (\({\small\tanh{z}}\)tanh(z)) (function template)[edit] | |
(C++11) | computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z}}\)arcosh(z)) (function template)[edit] |
(C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)[edit] |
| applies the functionstd::cosh to each element of valarray (function template)[edit] | |
C documentation forccosh | |
