Complex argument for scipy.special.ellipkinc

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December 08, 2019, at 11:30 AM

I am trying to calculate some mathematical expressions with the incomplete Legendre elliptic integral of the first kind:

Where K is the incomplete Legendre elliptic integral of the first kind. defined as ellipkinc in scipy.special.

Here is an example in Python:

from numpy import arccos, sqrt
from scipy.special import ellipkinc as K
z = (1+5j)/2.0
x = K(arccos(z), 1/sqrt(2))

But I get the following error:

TypeError                                 Traceback (most recent call last)
<ipython-input-12-d05df015ffeb> in <module>
----> 1 K(arccos(z), 1/sqrt(2))
TypeError: ufunc 'ellipkinc' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

Why this function does not accept a complex argument? if not, is there any alternative function in some package that accepts complex argument?

I appreciate any help.

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