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

Inverse hyperbolic cosine, elementwise.

Parameters :

x : array_like

Input array.

out : ndarray, optional

Array of the same shape as x, to store results in. See doc.ufuncs (Section “Output arguments”) for details.

Returns :

arccosh : ndarray

Array of the same shape as x.

See also

cosh, arcsinh, sinh, arctanh, tanh


arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi] and the real part in [0, inf].

For real-valued input data types, arccosh 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, arccosh is a complex analytical function that has a branch cut [-inf, 1] and is continuous from above on it.


[R2]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86.
[R3]Wikipedia, “Inverse hyperbolic function”,


>>> np.arccosh([np.e, 10.0])
array([ 1.65745445,  2.99322285])
>>> np.arccosh(1)

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