ATANH

Purpose:

Calculates the inverse hyperbolic tangent of any expression.

Syntax:

ATANH(val)

val

-

A scalar, series or table.

Returns:

A scalar, series, or table.

Example:

atanh(-1..0.01..1);gridhv;griddot

 

 

image\atanhpic01.gif

 

displays the inverse hyperbolic tangent from 1 to 1.

Example:

atanh(i)

 

returns 0 + 0.785398 i or (π/4)i.

Example:

atanh(-2..0.1..2)

 

returns a 41 point real series.

Remarks:

The inverse hyperbolic tangent is defined as:

 

image\atanh01.gif

 

for all complex z. The function is multi-valued and this definition places the branch cut in the complex plane at [-∞, -1] and [1, ∞].

 

For |x| > 1, atanh(x) returns a complex result.

 

SETDEGREE and SETRADIAN have no effect on this function because it always operates in radians.

See Also:

ACOSH

ACOTH

ASINH

ATAN

GATANH

TAN

TANH

TRIGONOMETRIC FUNCTIONS