IMSL C# Numerical Library

Complex.Acosh Method

Returns the inverse hyperbolic cosine (arc cosh) of a Complex, with a branch cut at values less than one along the real axis.

public static Complex Acosh(
Complex z
);

Parameters

z: A Complex object.

Return Value

A newly constructed Complex initialized to the inverse (arc) hyperbolic cosine of the argument. The real part of the result is non-negative and its imaginary part is in the interval $[-i\pi,i\pi]$ .

Remarks

Specifically, if z = x+iy,

$\acosh(\bar{z}) = \overline{\acosh(z)}$ .

$\acosh(\pm 0 + i0)$ returns $+0 + i\pi/2$ .

$\acosh(-\infty + i\infty )$ returns $+\infty + i3 \pi/4$ .

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

$\acosh(x + i\infty )$ returns $+\infty + i \pi/2$ , for finite x.

$\acosh(-\infty + iy)$ returns $+\infty + i \pi$ , for positive-signed finite y.

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

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

$\acosh(\pm \infty + i\NaN)$ returns $+\infty + i\NaN$ .

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

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

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

See Also

Complex Class | Imsl.Math Namespace