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Applicability of the $q$-Analogue of Zeilberger's Algorithm | | William Y.C. Chen
; Qing-Hu Hou
; Yan-Ping Mu
; | | Date: |
8 Oct 2004 | | Subject: | Combinatorics; Classical Analysis and ODEs MSC-class: 33F10; 68W30 | math.CO math.CA | | Abstract: | The 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. | | Source: | arXiv, math.CO/0410222 | | Services: | Forum | Review | PDF | Favorites | |
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