A Telescoping Algorithm for Double Summations

William Y. C. Chen *
Center for Combinatorics
Nankai University
Tianjin 300071, P. R. China

Abstract    Full Text PDF

Zeilberger's algorithm, also known as the method of "creative telescoping", has been widely used as a powerful tool to verify and discover hypergeometric identities. For single summations, Zeilberger's algorithm relies on Gosper's algorithm. We give an algorithm for double summations of hypergeometric terms. Given a hypergeometric term , we aim to find a differece operator

, and two rational functions such that Our algorithm works for the Andrews-Paule identity and Carlitz's identities.

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* This is joint work with Qing-Hu Hou and Yan-Ping Mu.