AN ALGORITHMIC PROOF THEORY FOR HYPERGEOMETRIC (ORDINARY AND Q) MULTISUM INTEGRAL IDENTITIES

• 成果类型: Article
• 署名作者: WILF, HS; ZEILBERGER, D
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF02100618
• 发表日期: 1992
• 页码: 575-633
• 关键词: summation; conjecture; series; POLYNOMIALS; systems; dyson; u(n)

摘要

It is shown that every 'proper-hypergeometric' multisum/integral identity, or q-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here. We give many examples of the method, including computer-generated proofs of identities of Mehta-Dyson, Selberg, Hille-Hardy, q-Saalschutz, and others. The prospect of using the method for proving multivariate identities that involve an arbitrary number of summations/integrations is discussed.