The Abel Lemma and the q-Gosper Algorithm

Details The Abel Lemma and the q-Gosper Algorithm The Abel Lemma and the q-Gosper Algorithm

2006-07-15

arxiv.org/abs/math/0607359v1

Mathematics

Combinatorics

17 pages

Scientific paper

Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's ${}_6\psi_6$ bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the ${}_6\psi_6$ sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the $q$-Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas.

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