Applicability of the -Analogue of Zeilberger's Algorithm
arXiv:math/0410222
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.
15 pages