Q-Gosper algorithm and simple Bailey pairs. (November 2022)

• Record Type: Journal Article
• Authors: Bian, Ke-Xin; Liu, Yue; Mu, Yan-Ping
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 39
• Page End: 52
• Publication Date: 2022-11
• Subjects: 33F10 -- 33D15; Simple Bailey pair -- q-Gosper algorithm -- q-Hypergeometric term; 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.2022.02.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a method of constructing simple Bailey pairs based on the q -Gosper algorithm. We illustrate the method by determining Gosper-summable q -hypergeometric terms of the form ( a ; q ) k ( q ; q ) k z k . We further give some simple Bailey pairs in more complicated forms. As applications, we derive some summation and transformation formulas for q -series.