Nonterminating Basic Hypergeometric Series and the $q$-Zeilberger Algorithm

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dc.creatorChen, William Y. C.
dc.creatorHou, Qing-Hu
dc.creatorMu, Yan-Ping
dc.date2005-09-13
dc.date.accessioned2026-07-07T05:23:09Z
dc.date.available2026-07-07T05:23:09Z
dc.descriptionWe present a systematic method for proving nonterminating basic hypergeometric identities. Assume that $k$ is the summation index. By setting a parameter $x$ to $xq^n$, we may find a recurrence relation of the summation by using the $q$-Zeilberger algorithm. This method applies to almost all nonterminating basic hypergeometric summation formulas in the book of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulas, including the Sears-Carlitz transformation, transformations of the very-well-poised $_8ϕ_7$ series, the Rogers-Fine identity, and the limiting case of Watson's formula that implies the Rogers-Ramanujan identities.
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/math/0509281
dc.identifierhttp://arxiv.org/abs/math/0509281
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76323
dc.subjectCombinatorics
dc.subject33D15, 33F10
dc.titleNonterminating Basic Hypergeometric Series and the $q$-Zeilberger Algorithm
dc.typetext

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