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Computer Proofs of a New Family of Harmonic Number Identities

By Scott Ahlgren, Peter Paule and Carsten Schneider


In this paper we consider ve conjectured harmonic number identities similar to those arising in the context of supercongruences for Apery numbers. The general object of this article is to discuss the possibility of automating not only the proof but also the discovery of such formulas. As a specic application we consider two dierent algorithmic methods to derive and to prove the ve conjectured identities. One is based on an extension of Karr's summation algorithm in dierence elds. The other method combines an old idea of Newton (which has been extended by Andrews) with Zeilberger's algorithm for denite hypergeometric sums

Year: 2002
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