I've needed these in implementing some equations derived by
Mathematica which don't assume [0,1]-bound (nor real) parameters.
Along these lines, please find attached a couple of functions
(complete integrals for K, E, and PI) that I've started with; these
are based on "connection formulae" here: <http://dlmf.nist.gov/19.7>.
I hope this helps. I'll let you know if I do any more work in this
area.
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to pelliptic
One thing on the implementation in the ellip.m
If you're planed to use it with matrix/tensor inputs you'll better
implement it with matrix and array arithmetic in Matlab.