NAME¶

std::cosh(std::complex) - std::cosh(std::complex)

Synopsis¶

Defined in header <complex>
template< class T > (since C++11)
complex<T> cosh( const complex<T>& z );

Computes complex hyperbolic cosine of a complex value z.

Parameters¶

z - complex value

Return value¶

If no errors occur, complex hyperbolic cosine of z is returned

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

* std::cosh(std::conj(z)) == std::conj(std::cosh(z))
* std::cosh(z) == std::cosh(-z)
* If z is (+0,+0), the result is (1,+0)
* If z is (+0,+∞), the result is (NaN,±0) (the sign of the imaginary part is
unspecified) and FE_INVALID is raised
* If z is (+0,NaN), the result is (NaN,±0) (the sign of the imaginary part is
unspecified)
* If z is (x,+∞) (for any finite non-zero x), the result is (NaN,NaN) and
FE_INVALID is raised
* If z is (x,NaN) (for any finite non-zero x), the result is (NaN,NaN) and
FE_INVALID may be raised
* If z is (+∞,+0), the result is (+∞,+0)
* If z is (+∞,y) (for any finite non-zero y), the result is +∞cis(y)
* If z is (+∞,+∞), the result is (±∞,NaN) (the sign of the real part is
unspecified) and FE_INVALID is raised
* If z is (+∞,NaN), the result is (+∞,NaN)
* If z is (NaN,+0), the result is (NaN,±0) (the sign of the imaginary part is
unspecified)
* If z is (NaN,+y) (for any finite non-zero y), the result is (NaN,NaN) and
FE_INVALID may be raised
* If z is (NaN,NaN), the result is (NaN,NaN)

where cis(y) is cos(y) + i sin(y)

Notes¶

Mathematical definition of hyperbolic cosine is cosh z =

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

Examples¶

// Run this code

#include <iostream>
#include <cmath>
#include <complex>

int main()
{
std::cout << std::fixed;
std::complex<double> z(1, 0); // behaves like real cosh along the real line
std::cout << "cosh" << z << " = " << std::cosh(z)
<< " (cosh(1) = " << std::cosh(1) << ")\n";

std::complex<double> z2(0, 1); // behaves like real cosine along the imaginary line
std::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)

See also¶

computes hyperbolic sine of a complex number (\({\small\sinh{z}
sinh(std::complex) }\)sinh(z))
(function template)
computes hyperbolic tangent of a complex number
tanh(std::complex) (\({\small\tanh{z} }\)tanh(z))
(function template)
acosh(std::complex) computes area hyperbolic cosine of a complex number
(C++11) (\({\small\operatorname{arcosh}{z} }\)arcosh(z))
(function template)
cosh
coshf computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x))
coshl (function)
(C++11)
(C++11)
cosh(std::valarray) applies the function std::cosh to each element of valarray
(function template)