Applicability of the q-analogue of Zeilberger's algorithm

作者：Chen WYC^*; Hou QH; Mu YP

来源：Journal of Symbolic Computation, 2005, 39(2): 155-170.

DOI：10.1016/j.jsc.2004.09.002

• Zeilberger's algorithm
• q-hypergeometric term
• Z-pair
• qZ-pair
• proper hypergeometric term
• q-proper hypergeometric term

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 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 qZ-pair.

• 出版日期2005-2
• 单位南开大学