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 6ψ6 bilateral summation formula. In other words, the Abel
lemma spells out the telescoping nature of the 6ψ6 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.
Keywords: the Abel lemma, Abel pairs, basic hypergeometric series, the q-Gosper algorithm, Gosper pairs.