Applicability of the $q$-Analogue of Zeilberger's Algorithm

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dc.creatorChen, William Y. C.
dc.creatorHou, Qing-Hu
dc.creatorMu, Yan-Ping
dc.date2004-10-08
dc.date.accessioned2026-07-07T05:13:05Z
dc.date.available2026-07-07T05:13:05Z
dc.descriptionThe applicability or terminating condition for the ordinary case of Zeilberger's algorithm was recently obtained by Abramov. For the $q$-analogue, the question of whether a bivariate $q$-hypergeometric term has a $qZ$-pair remains open. Le has found a solution to this problem when the given bivariate $q$-hypergeometric term is a rational function in certain powers of $q$. We solve the problem for the general case by giving a characterization of bivariate $q$-hypergeometric terms for which the $q$-analogue of Zeilberger's algorithm terminates. Moreover, we give an algorithm to determine whether a bivariate $q$-hypergeometric term has a $qZ$-pair.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0410222
dc.identifierhttp://arxiv.org/abs/math/0410222
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72814
dc.subjectCombinatorics
dc.subjectClassical Analysis and ODEs
dc.subject33F10; 68W30
dc.titleApplicability of the $q$-Analogue of Zeilberger's Algorithm
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