Comment #1 on issue 2063 by asmeurer: Add complete elliptic integrals http://code.google.com/p/sympy/issues/detail?id=2063
Well, docstrings would be nice. I only know a very little about elliptic integrals, so I was being confused on which of EllipticK and EllipticE corresponded to which in http://en.wikipedia.org/wiki/Elliptic_integrals (I am assuming the functions in the Wikipedia article correspond to K(x) and E(x), respectively). Just a simple one for each giving a definition and a reference to MathWorld or Wikipedia or something like that would be fine, I think.
What was the identity you didn't finish writing in EllipticK.eval? I didn't notice any in MathWorld or Wikipedia for EllipticK(I*x). Maybe put it in the comments.
As far as the code goes, except for the lack of docstrings, I think it looks fine. But, of course, it would be nice for someone to actually verify the mathematical correctness of everything too :)
Go ahead and press the "Pull Request" button in GitHub and send it to sympy/sympy:master.
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