[seqfan] Probable Omission

Brad Klee bradklee at gmail.com
Thu Jan 30 02:17:06 CET 2020

CoefficientList[Series[2/Pi EllipticPi[4 x, 16 y],
   {x, 0, 20}, {y, 0, 20}], {x, y}] // TableForm
(see also: http://functions.wolfram.com/EllipticIntegrals/EllipticPi/06/01/03/ )
Read by anti-diagonals: 1, 2, 4, 6, 12, 36, 20, 40, 120, 400, . . .
Columns appear as translates of A001700, to an integer multiple.

Is this table in OEIS somehow?

Perhaps we have forgotten the complete elliptic integral of the third
kind because the Legendre theory is too unwieldy, with too few
examples worked in public.

Earlier we found out that A006480 is an elliptic integral strongly
comparable to A002894. This would be a good starting place.
Is there a Legendre decomposition? If so, how is it found?

Another vexing problem.


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