arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

Inverse hyperbolic sine 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
    :ref:`ufunc docs <ufuncs.kwargs>`.

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
----------
.. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
       10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
.. [2] Wikipedia, "Inverse hyperbolic function",
       http://en.wikipedia.org/wiki/Arcsinh

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