Swisher对Van Hamme （E.2）和（F.2）超同余和两个超同余的改进

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-13 DOI:10.1016/j.jmaa.2025.129673

Victor J.W. Guo , Chen Wang

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引用次数: 0

摘要

1997年，Van Hamme提出了截断超几何级数上的13个超同余。Van Hamme （B.2）的超同余首先由Mortenson证实，后来由Zudilin得到WZ证明。2012年，Sun再次使用WZ方法，将Van Hamme的（B.2）超同余扩展到模数p4的情况，其中p是奇素数。本文利用一个更一般的WZ对，将Hamme的（E.2）和（F.2）超同余，以及Swisher的两个超同余推广到模数p4的情况。我们对这些超同余的推广与欧拉多项式有关。我们还提出了一个关于q超同余的相关猜想，以供进一步研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Refinements of Van Hamme's (E.2) and (F.2) supercongruences and two supercongruences by Swisher

In 1997, Van Hamme proposed 13 supercongruences on truncated hypergeometric series. Van Hamme's (B.2) supercongruence was first confirmed by Mortenson and received a WZ proof by Zudilin later. In 2012, using the WZ method again, Sun extended Van Hamme's (B.2) supercongruence to the modulus

p^{4}

case, where p is an odd prime. In this paper, by using a more general WZ pair, we generalize Hamme's (E.2) and (F.2) supercongruences, as well as two supercongruences by Swisher, to the modulus

p^{4}

case. Our generalizations of these supercongruences are related to Euler polynomials. We also put forward a relevant conjecture on a q-supercongruence for further study.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.