Applicability of the q-Analogue of Zeilberger's Algorithm

William Y.C. Chen, Qing-Hu Hou and Yan-Ping Mu

  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 char- acterization 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.

  AMS Classification:  33F10, 68W30.

  Keywords:  Zeilberger's algorithm, q-hypergeometric term, Z-pair, qZ-pair, proper hypergeometric term, q-proper hypergeometric term.