English

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

Combinatorics 2007-05-23 v1 Classical Analysis and ODEs

Abstract

The applicability or terminating condition for the ordinary case of Zeilberger's algorithm was recently obtained by Abramov. For the qq-analogue, the question of whether a bivariate qq-hypergeometric term has a qZqZ-pair remains open. Le has found a solution to this problem when the given bivariate qq-hypergeometric term is a rational function in certain powers of qq. We solve the problem for the general case by giving a characterization of bivariate qq-hypergeometric terms for which the qq-analogue of Zeilberger's algorithm terminates. Moreover, we give an algorithm to determine whether a bivariate qq-hypergeometric term has a qZqZ-pair.

Keywords

Cite

@article{arxiv.math/0410222,
  title  = {Applicability of the $q$-Analogue of Zeilberger's Algorithm},
  author = {William Y. C. Chen and Qing-Hu Hou and Yan-Ping Mu},
  journal= {arXiv preprint arXiv:math/0410222},
  year   = {2007}
}

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15 pages