{"title":"A new extension of a “divergent” Ramanujan-type supercongruence","authors":"Jian Cao, Victor J. W. Guo, Xiao Yu","doi":"10.1080/10236198.2023.2270536","DOIUrl":null,"url":null,"abstract":"AbstractWe give a new extension of a ‘divergent’ Ramanujan-type supercongruence of Guillera and Zudilin by establishing a q-analogue of this result. Our proof makes use of the ‘creative microscoping’ method, which was introduced by the second author and Zudilin in 2019. We also present a similar extension of the (L.2) supercongruence of Van Hamme in the modulus p2 case.Keywords: Supercongruencebasic hypergeometric seriescyclotomic polynomialscreative microscoping2020 Mathematics Subject Classifications: 33D1511A0711B65 Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"54 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Difference Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2270536","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractWe give a new extension of a ‘divergent’ Ramanujan-type supercongruence of Guillera and Zudilin by establishing a q-analogue of this result. Our proof makes use of the ‘creative microscoping’ method, which was introduced by the second author and Zudilin in 2019. We also present a similar extension of the (L.2) supercongruence of Van Hamme in the modulus p2 case.Keywords: Supercongruencebasic hypergeometric seriescyclotomic polynomialscreative microscoping2020 Mathematics Subject Classifications: 33D1511A0711B65 Disclosure statementNo potential conflict of interest was reported by the author(s).
期刊介绍：
Journal of Difference Equations and Applications presents state-of-the-art papers on difference equations and discrete dynamical systems and the academic, pure and applied problems in which they arise. The Journal is composed of original research, expository and review articles, and papers that present novel concepts in application and techniques.
The scope of the Journal includes all areas in mathematics that contain significant theory or applications in difference equations or discrete dynamical systems.
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