Christian Krattenthaler and
C. Schneider
Evaluation of binomial double sums involving absolute values
(36 pages)
Abstract.
We show that double sums of the form
$$
\sum_{i,j=-n} ^{n}
|i^sj^t(i^k-j^k|^\beta \binom {2n} {n+i} \binom {2n} {n+j}
$$
can always be expressed in terms of
a linear combination of just four functions, namely
$\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, 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.
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