std::sinh(std::complex) - cppreference.com (original) (raw)

| | | | | -------------------------------------------------------------- | | ------------- | | template< class T > complex<T> sinh( const complex<T>& z ); | | (since C++11) |

Computes complex hyperbolic sine of a complex value z.

Contents

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 See also

[edit] Parameters

[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 z is (+0,+0), the result is (+0,+0)
• If z is (+0,+∞), the result is (±0,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is (+0,NaN), the result is (±0,NaN)
• If z is (x,+∞) (for any positive finite x), the result is (NaN,NaN) and FE_INVALID is raised
• If z is (x,NaN) (for any positive finite 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 positive finite 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) (the sign of the real part is unspecified)
• If z is (NaN,+0), the result is (NaN,+0)
• If z is (NaN,y) (for any finite nonzero 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

Mathematical definition of hyperbolic sine is sinh z = .

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

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