numpy.arcsinh(x[, out])

Inverse hyperbolic sine elementwise.


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.


out : ndarray

Array of of the same shape as x.


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.


[R8]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86.
[R9]Wikipedia, “Inverse hyperbolic function”,


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

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