std::sinh(std::complex)
From cppreference.com
| Defined in header <complex>
|
||
| template< class T > complex<T> sinh( const complex<T>& z ); |
(since C++11) | |
Computes complex hyperbolic sine of a complex value z.
Contents |
[edit] Parameters
| z | - | complex value |
[edit] Return value
If no errors occur, complex hyperbolic sine 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::sinh(std::conj(z)) == std::conj(std::sinh(z))
- std::sinh(z) == -std::sinh(-z)
- If
zis(+0,+0), the result is(+0,+0) - If
zis(+0,+∞), the result is(±0,NaN)(the sign of the real part is unspecified) and FE_INVALID is raised - If
zis(+0,NaN), the result is(±0,NaN) - If
zis(x,+∞)(for any positive finite x), the result is(NaN,NaN)and FE_INVALID is raised - If
zis(x,NaN)(for any positive finite x), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(+∞,+0), the result is(+∞,+0) - If
zis(+∞,y)(for any positive finite y), the result is(+∞,cis(y)) - If
zis(+∞,+∞), the result is(±∞,NaN)(the sign of the real part is unspecified) and FE_INVALID is raised - If
zis(+∞,NaN), the result is(±∞,NaN)(the sign of the real part is unspecified) - If
zis(NaN,+0), the result is(NaN,+0) - If
zis(NaN,y)(for any finite nonzero y), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(NaN,NaN), the result is(NaN,NaN)
where cis(y) is cos(y) + i sin(y)
[edit] Notes
Mathematical definition of hyperbolic sine is sinh z =| ez -e-z |
| 2 |
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 period 2πi
[edit] Example
Run this code
#include <iostream> #include <cmath> #include <complex> int main() { std::cout << std::fixed; std::complex<double> z(1, 0); // behaves like real sinh along the real line std::cout << "sinh" << z << " = " << std::sinh(z) << " (sinh(1) = " << std::sinh(1) << ")\n"; std::complex<double> z2(0, 1); // behaves like sine along the imaginary line std::cout << "sinh" << z2 << " = " << std::sinh(z2) << " ( sin(1) = " << std::sin(1) << ")\n"; }
Output:
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
| computes hyperbolic cosine of a complex number (ch(z)) (function template) | |
| computes hyperbolic tangent of a complex number (function template) | |
| (C++11) |
computes area hyperbolic sine of a complex number (function template) |
| computes hyperbolic sine (sh(x)) (function) | |
| applies the function std::sinh to each element of valarray (function template) | |
| C documentation for csinh
| |