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 q Z -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 q Z -pair.
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