| In this paper, the folio wings are introduced briefly: holonomic theory; the basic idea that D.Zeilberger used to prove identities using holonomic theory. And Wu method is generalized to the non-commutative Weyl algebra . Furthermore, dialytic method of elimination is replaced by Wu method, so the prove can be extended from the single-variable hypergeometric identities to multi-variable ones.The main work of the paper is summarized as followings: the algorithm is improved somewhat, the algorithm is implemented in PC by Mathematica software and the effectivity is proved to by testing all the examples that have been proved by D.Zeilberg and H.Wilf using WZ-pair method and testing many identities of the book named "Combinatorial Identities", which was written by H.W.Gould in 1972. |
