Semi-automated proof of supercongruences on partial sums of hypergeometric series. (July 2019)

• Record Type: Journal Article
• Authors: Liu, Ji-Cai
• Is Part Of: Journal of symbolic computation. Volume 93(2019)
• Page Start: 221
• Page End: 229
• Publication Date: 2019-07
• Subjects: Combinatorial identities -- Supercongruences -- Euler numbers -- Harmonic numbers; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Using the software packageSigma developed by Schneider, we automatically discover and prove some combinatorial identities involving harmonic numbers, from which we deduce some supercongruences on partial sums of hypergeometric series. These results confirm some conjectural generalizations of van Hamme's supercongruences in some special cases, which were recently proposed byGuo (2017) .