Q-Rational reduction and q-analogues of series for π. (May 2023)

• Record Type: Journal Article
• Authors: Wang, Rong-Hua; Zhong, Michael X.X.
• Is Part Of: Journal of symbolic computation. Volume 116(2023)
• Page Start: 58
• Page End: 71
• Publication Date: 2023-05
• Subjects: Summability -- Rational reduction -- Series for π; 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.2022.08.020
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we present a q -analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the q -Gosper representation, we describe the structure of rational functions that are summable when multiplied with a given q -hypergeometric term. The structure theorem enables us to generalize the q -polynomial reduction to the rational case, which can be used in the automatic proof and discovery of q -identities. As applications, several q -analogues of series for π are presented.