“发散”拉马努金型超同余的新扩展

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Journal of Difference Equations and Applications Pub Date : 2023-10-17 DOI:10.1080/10236198.2023.2270536

Jian Cao, Victor J. W. Guo, Xiao Yu

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引用次数: 0

摘要

摘要通过建立Guillera和Zudilin的“发散”ramanujan型超同余的q-类似，给出了该结果的一个新的推广。我们的证明使用了由第二作者和祖德林在2019年提出的“创造性显微镜”方法。在模p2情况下，我们也给出了Van Hamme (L.2)超同余的一个类似推广。关键词:超同余;基本超几何级数;分环多项式;;创造性显微镜;;;

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A new extension of a “divergent” Ramanujan-type supercongruence

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).

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来源期刊

Journal of Difference Equations and Applications 数学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

4-8 weeks

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.