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Further double sums of Dunkl and Gasper. (English) Zbl 1371.05023

Summary: By combining the series rearrangement with a reformulation of Beta function, we prove a transformation theorem that reduces a double sum with seven free parameters to a terminating hypergeometric \({_4F_3}\)-series. Seven double sum identities are derived as consequences with one of them extending the recent double sum of C. F. Dunkl and P. B. Gasper [“The sums of a double hypergeometric series and of the first \(m+1\) terms of \(_3F_2(a,b,c;(a+b+1)/2,2c;1)\) when \(c=-m\) is a negative integer”, Preprint, arXiv:1412.4022].

MSC:

05A19 Combinatorial identities, bijective combinatorics
33C20 Generalized hypergeometric series, \({}_pF_q\)

Software:

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References:

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