std::asinh(std::complex)

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std::complex
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 real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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 Defined in header template< class T > complex asinh( const complex& z ); (since C++11)

Computes complex arc hyperbolic sine of a complex value z with branch cuts outside the interval [−i; +i] along the imaginary axis.

Contents

Parameters

 z - complex value

Return value

If no errors occur, the complex arc hyperbolic sine of z is returned, in the range of a strip mathematically unbounded along the real axis and in the interval [−iπ/2; +iπ/2] along the imaginary axis.

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• std::asinh(std::conj(z)) == std::conj(std::asinh(z))
• std::asinh(-z) == -std::asinh(z)
• If z is (+0,+0), the result is (+0,+0)
• If z is (x,+∞) (for any positive finite x), the result is (+∞,π/2)
• If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (+∞,y) (for any positive finite y), the result is (+∞,+0)
• If z is (+∞,+∞), the result is (+∞,π/4)
• If z is (+∞,NaN), the result is (+∞,NaN)
• 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,+∞), the result is (±∞,NaN) (the sign of the real part is unspecified)
• If z is (NaN,NaN), the result is (NaN,NaN)