Complex.Atanh Method

Returns the inverse hyperbolic tangent (arc tanh) of a Complex, with branch cuts outside the interval [-1,1] on the real axis.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

Copy

public static Complex Atanh(
	Complex z
)

Public Shared Function Atanh ( 
	z As Complex
) As Complex

public:
static Complex Atanh(
	Complex z
)

static member Atanh : 
        z : Complex -> Complex

Parameters

z: Type: Imsl.Math.Complex
A Complex object.

Return Value

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

Remarks

Specifically, if z = x+iy,

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

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

$\atanh(+\infty + i\infty )$ returns $+0 + i\pi/2$ .

$\atanh(+\infty + iy)$ returns $+0 + i\pi/2$ , for finite positive-signed y.

$\atanh(x + i\infty )$ returns $+0 + i\pi/2$ , for finite positive-signed x.

$\atanh(+0 + i\NaN)$ returns $+0 + i\NaN$ .

$\atanh(\NaN + i\infty )$ returns $\pm 0 + i pi/2$ (where the sign of the real part of the result is unspecified).

$\atanh(+\infty + i\NaN)$ returns $+0 + i\NaN$ .

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

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

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

Reference

Complex Structure

Imsl.Math Namespace