Evaluation of binomial double sums involving absolute values

07/18/2016

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by   Christian Krattenthaler, et al.

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We show that double sums of the form ∑_i,j=-n ^n |i^sj^t(i^k-j^k)^β| 2nn+i2nn+j can always be expressed in terms of a linear combination of just four functions, namely 4n2n, 2nn^2, 4^n2nn, and 16^n, with coefficients that are rational in n. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals.