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# numpy.arctanh

`numpy.``arctanh`(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctanh'>

  Inverse hyperbolic tangent element-wise.

  Parameters: | x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the ufunc docs.
  Returns: | out : ndarray Array of the same shape as x.

  See also

  `emath.arctanh`

  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

  [R7] | M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

  [R8] | Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh

  Examples

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