A further common <i>q</i>-generalization of the (B.2) and (C.2) supercongruences of Van Hamme

In 2019, the author and Zudilin gave a parametric q-supercongruence, which is a common generalization of the (B.2) and (C.2) supercongruences of Van Hamme. In this paper, we further give a generalization of this q-supercongruence. As a corollary, we obtain the following supercongruence: for any prime [Formula: see text], positive integer r, and nonnegative integer [Formula: see text], [Formula: see text]

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Publication Details

Journal
International Journal of Number Theory
Published
2024-09-30
DOI
https://doi.org/10.1142/s1793042125500290
Citations
4
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
5.08
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article

A further common q-generalization of the (B.2) and (C.2) supercongruences of Van Hamme

Victor J. W. Guo
4 citations
International Journal of Number Theory
Advanced Mathematical Identities
5.08
article

A further common q-generalization of the (B.2) and (C.2) supercongruences of Van Hamme

Victor J. W. Guo
article en
4 citations

Abstract

In 2019, the author and Zudilin gave a parametric q-supercongruence, which is a common generalization of the (B.2) and (C.2) supercongruences of Van Hamme. In this paper, we further give a generalization of this q-supercongruence. As a corollary, we obtain the following supercongruence: for any prime [Formula: see text], positive integer r, and nonnegative integer [Formula: see text], [Formula: see text]

International Journal of Number TheoryVol. 21(03)
Hangzhou Normal University (CN)
Openalex Percentile: Top 4%
Advanced Mathematical Identities
5.08
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