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.

  AMS Classification:   33D15, 33F10

  Keywords:   the Abel lemma, Abel pairs, basic hypergeometric series, the q-Gosper algorithm, Gosper pairs

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