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: 6.5.0.0

Syntax

C#
public static Complex Atanh(
	Complex z
)
Visual Basic (Declaration)
Public Shared Function Atanh ( _
	z As Complex _
) As Complex
Visual C++
public:
static Complex Atanh(
	Complex z
)

Parameters

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

Return Value

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 +0 + i0.

\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.

See Also