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The Abel Lemma and the q-Gosper Algorithm

Vincent Y. B. Chen·William Y. C. Chen·Nancy S. S. Gu
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Abstract

Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's ${}_6ψ_6$ bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the ${}_6ψ_6$ 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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Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu. 2006-07-15. The Abel Lemma and the q-Gosper Algorithm. https://arxiv.org/abs/math/0607359

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