2004/10/08 by William Y. C. Chen, Chen, William Y. C., Qing-Hu Hou +3
Mathematics · #33F10 #68W30 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #math.CA #math.CO #msc:33F10 #msc:68W30
paper · pdf · doi:10.48550/arxiv.math/0410222
15 pages
arxiv created 2004/10/08 · arxiv updated 2009/12/01
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.