Difference between revisions of "cpp/numeric/complex/cosh"

Latest revision as of 23:13, 21 April 2023

Computes complex hyperbolic cosine of a complex value z.

[edit] Parameters

[edit] Return value

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

[edit] 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).

[edit] Notes

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.

[edit] Examples

#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 line
    std::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 line
    std::cout << "cosh" << z2 << " = " << std::cosh(z2)
              << " ( cos(1) = " << std::cos(1) << ")\n";
}

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)

[edit] See also