Complex.Asinh Method

Returns the inverse hyperbolic sine (arc sinh) of a Complex, with branch cuts outside the interval [-i,i].

public static Complex Asinh(
Complex z
);

Parameters

z: A Complex object.

Return Value

A newly constructed Complex initialized to the inverse (arc) hyperbolic sine of the argument. Its imaginary part is in the interval $[-i\pi/2,i\pi/2]$ .

Remarks

Specifically, if z = x+iy,

$\asinh(\bar{z}) = \overline{\asinh(z)}$ and asinh is odd.

$\asinh(+0 + i0)$ returns .

$\asinh(\infty + i\infty )$ returns $+\infty + i \pi/4$ .

$\asinh(x + i\infty )$ returns $+\infty + i \pi/2$ for positive-signed finite x.

$\asinh(+\infty + iy)$ returns $+\infty + i0$ for positive-signed finite y.

$\asinh(\NaN + i\infty )$ returns $\pm \infty + i\NaN$ (where the sign of the real part of the result is unspecified).

$\asinh(+\infty + i\NaN)$ returns $+\infty + i\NaN$ .

$\asinh(\NaN + i0)$ returns $\NaN + i0$ .

$\asinh(\NaN + iy)$ returns $\NaN + i\NaN$ , for finite nonzero y.

$\asinh(x + i\NaN)$ returns $\NaN + i\NaN$ , for finite x.

$\asinh(\NaN + i\NaN)$ returns $\NaN + i\NaN$ .

Complex.Asinh Method

Parameters

Return Value

Remarks

See Also