atanh hyperbolic tangent inverse

## Syntax

    t = atanh(x)

## Arguments

x, t

  Arrays of real or complex numbers, of same sizes.

## Description

The components of vector `t` are the hyperbolic tangent inverse of the corresponding entries of vector `x`. The result `t` is real for `x` in `[-1,1]`, and complex otherwise.

## Examples

With input real numbers:

    x = [-%inf -2 -1 -0.5 0 0.5 1 2 3 %inf];
    [x ; atanh(tanh(x))]
    atanh(x')

    --> [x ; atanh(tanh(x))]
     ans  =
      -Inf  -2.  -1.  -0.5   0.   0.5   1.   2.   3.   Inf
      -Inf  -2.  -1.  -0.5   0.   0.5   1.   2.   3.   Inf

    --> atanh(x')
     ans  =
       0.        + 1.5707963i
      -0.5493061 + 1.5707963i
      -Inf       + 0.i
      -0.5493061 + 0.i
       0.        + 0.i
       0.5493061 + 0.i
       Inf       + 0.i
       0.5493061 + 1.5707963i
       0.3465736 + 1.5707963i
       0.        + 1.5707963i

With input complex numbers:

    x = [-1-%i, -%i, 0, %i, %i+1];
    [x; tanh(atanh(x)) ; atanh(tanh(x))]
    atanh(x.')

    --> [x; tanh(atanh(x)) ; atanh(tanh(x))]
     ans  =

      -1. - i     0. - i     0. + 0.i   0. + i     1. + i
      -1. - i     0. - i     0. + 0.i   0. + i     1. + i
      -1. - i     0. - i     0. + 0.i   0. + i     1. + i

    --> atanh(x.')
     ans  =

      -0.4023595 - 1.017222i
       0.        - 0.7853982i
       0.        + 0.i
       0.        + 0.7853982i
       0.4023595 + 1.017222i

## See also

- tanh

## History

6.0

- `atanh(-1)` is now always `-Inf`, and `atanh(1)` always `Inf`.
- For any real x>1, imag(atanh(x)) is now > 0.