The Abel Lemma and the q-Gosper Algorithm
Vincent Y.B. Chen, William Y.C. Chen and Nancy S.S. Gu
Abstract: Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's _{6}ψ_{6} bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the _{6}ψ_{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. AMS Classification: 33D15, 33F10 Keywords: the Abel lemma, Abel pairs, basic hypergeometric series, the q-Gosper algorithm, Gosper pairs Download: pdf |