The Abel Lemma and the q-Gosper Algorithm

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dc.creatorChen, Vincent Y. B.
dc.creatorChen, William Y. C.
dc.creatorGu, Nancy S. S.
dc.date2006-07-15
dc.date.accessioned2026-07-07T07:18:24Z
dc.date.available2026-07-07T07:18:24Z
dc.descriptionChu 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.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0607359
dc.identifierhttp://arxiv.org/abs/math/0607359
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114286
dc.subjectCombinatorics
dc.subjectClassical Analysis and ODEs
dc.titleThe Abel Lemma and the q-Gosper Algorithm
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