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# numpy.arctanh

`numpy.``arctanh`(x[, out])

  Inverse hyperbolic tangent elementwise.

  Parameters: | x : array_like Input array.
  Returns: | out : ndarray Array of the same shape as x.

  Notes

  arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2].

  For real-valued input data types, arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields `nan` and sets the invalid floating point error flag.

  For complex-valued input, arctanh is a complex analytical function that has branch cuts [-1, -inf] and [1, inf] and is continuous from above on the former and from below on the latter.

  The inverse hyperbolic tangent is also known as atanh or `tanh^-1`.

  References

  [14] | M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

  [15] | Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh

  Examples

      >>> np.arctanh([0, -0.5])
      array([ 0.        , -0.54930614])

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