On the existence of telescopers for mixed hypergeometric terms. (May 2015)

• Record Type: Journal Article
• Authors: Chen, Shaoshi; Chyzak, Frédéric; Feng, Ruyong; Fu, Guofeng; Li, Ziming
• Is Part Of: Journal of symbolic computation. Volume 68:Part 1(2015)
• Page Start: 1
• Page End: 26
• Publication Date: 2015-05
• Subjects: Creative telescoping -- Zeilberger's algorithms -- Existence criteria; 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.2014.08.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on additive and multiplicative decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed hypergeometric inputs, and to verify that certain indefinite sums do not satisfy any polynomial differential equation.