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# numpy.arcsinh

`numpy.``arcsinh`(x[, out]) = <ufunc 'arcsinh'>

  Inverse hyperbolic sine element-wise.

  Parameters : | x : array_like Input array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See `doc.ufuncs`.
  Returns : | out : ndarray Array of of the same shape as x.

  Notes

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

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

  For complex-valued input, `arccos` is a complex analytical function that has branch cuts [1j, infj] and [-1j, -infj] and is continuous from the right on the former and from the left on the latter.

  The inverse hyperbolic sine is also known as asinh or `sinh^-1`.

  References

  [R4] | M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

  [R5] | Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arcsinh

  Examples

      >>> np.arcsinh(np.array([np.e, 10.0]))
      array([ 1.72538256,  2.99822295])