Proof of the Wilf–Zeilberger conjecture for mixed hypergeometric terms. (July 2019)

• Record Type: Journal Article
• Authors: Chen, Shaoshi; Koutschan, Christoph
• Is Part Of: Journal of symbolic computation. Volume 93(2019)
• Page Start: 133
• Page End: 147
• Publication Date: 2019-07
• Subjects: Wilf–Zeilberger conjecture -- Hypergeometric term -- Properness -- Holonomic function -- D-finite function -- Ore–Sato theorem; 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.2018.06.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuous variables is holonomic if and only if it is proper. Strictly speaking the conjecture does not hold, but it is true when reformulated properly: Payne proved a piecewise interpretation in 1997, and independently, Abramov and Petkovšek in 2002 proved a conjugate interpretation. Both results address the pure discrete case of the conjecture. In this paper we extend their work to hypergeometric terms in several discrete and continuous variables and prove the conjugate interpretation of the Wilf–Zeilberger conjecture in this mixed setting.