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 -analogue, the question of whether a bivariate -hypergeometric term has a -pair remains open. Le has found a solution to this problem when the given bivariate -hypergeometric term is a rational function in certain powers of . We solve the problem for the general case by giving a characterization of bivariate -hypergeometric terms for which the -analogue of Zeilberger's algorithm terminates. Moreover, we give an algorithm to determine whether a bivariate -hypergeometric term has a -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}
}
Comments
15 pages