Computational Methods and Function Theory 8 (2008), No. 2, 531--544
Copyright Heldermann Verlag 2008
Richard R. Hall
rrh1@york.ac.uk , York University, Mathematics Department, Heslington, York YO10 5DD, U.K.
Simultaneous identities involving elliptic integrals of the first and second kinds, evaluated at the roots of a very simple trigonometric polynomial, are given. There are two parameters m∈N, k∈R+ and just the cases m=1,2,3,4 are treated, the remainder being offered as a problem. The identities originate in the evaluation of some trigonometric integrals which start the paper.
Keywords: Elliptic integral, Jacobian, trigonometric.
MSC 2000: 33E05.
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