atanh

Inverse hyperbolic tangent

Syntax

`Y = atanh(X)`

Description

The `atanh` function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

`Y = atanh(X)` returns the inverse hyperbolic tangent for each element of `X`.

Examples

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Graph of Inverse Hyperbolic Tangent Function

Graph the inverse hyperbolic tangent over the domain .

```x = -0.99:0.01:0.99; plot(x,atanh(x)), grid on ```

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Inverse Hyperbolic Tangent

The inverse hyperbolic tangent can be defined as

${\mathrm{tanh}}^{-1}\left(z\right)=\frac{1}{2}\mathrm{log}\left(\frac{1+z}{1-z}\right).$