Abstract
In this paper, the following are introduced briefly: the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non-commutative Weyl algebra. We give an algorithm for proving the single-variable q-proper-hypergeometric identities that is based on Zeilberger’s approach and the elimination in Weyl algebra. Finally, we test several examples that have been proven by D. Zeilberger and H. Wilf using the WZ-pair method and Gosper algorithm.
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