** 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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