The Abel Lemma and the q-Gosper Algorithm

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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.
17 pages

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Combinatorics, Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/114286

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607359
 http://arxiv.org/abs/math/0607359

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arXiv