Common mathematical functions | |||||||||||||||||||||||||||||||
Mathematical special functions(C++17) | |||||||||||||||||||||||||||||||
Mathematical constants(C++20) | |||||||||||||||||||||||||||||||
Basic linear algebra algorithms(C++26) | |||||||||||||||||||||||||||||||
Data-parallel types (SIMD)(C++26) | |||||||||||||||||||||||||||||||
Floating-point environment(C++11) | |||||||||||||||||||||||||||||||
Complex numbers | |||||||||||||||||||||||||||||||
Numeric array (valarray ) | |||||||||||||||||||||||||||||||
Pseudo-random number generation | |||||||||||||||||||||||||||||||
Bit manipulation(C++20) | |||||||||||||||||||||||||||||||
Saturation arithmetic(C++26) | |||||||||||||||||||||||||||||||
Factor operations | |||||||||||||||||||||||||||||||
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Interpolations | |||||||||||||||||||||||||||||||
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Generic numeric operations | |||||||||||||||||||||||||||||||
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C-style checked integer arithmetic | |||||||||||||||||||||||||||||||
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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 |