A new extension of a "divergent" Ramanujan-type supercongruence

被引：0
|
作者：
Cao, Jian [1 ]
Guo, Victor J. W. [2 ]
Yu, Xiao [1 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou, Peoples R China
[2] Huaiyin Normal Univ, Sch Math & Stat, Huaian 223300, Peoples R China
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2024年 / 30卷 / 01期
关键词：
Supercongruence; basic hypergeometric series; cyclotomic polynomials; creative microscoping;
D O I：
10.1080/10236198.2023.2270536
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We 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 $ p<^>2 $ p2 case.
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页码：122 / 132
页数：11
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