New $ q $-supercongruences arising from a summation of basic hypergeometric series

Chuanan Wei; Chun Li; Chuanan Wei; Chun Li

doi:10.3934/math.2022228

AIMS Mathematics

2022, Volume 7, Issue 3: 4125-4136. doi: 10.3934/math.2022228

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New $ q $-supercongruences arising from a summation of basic hypergeometric series

Chuanan Wei ^1,2,3,
Chun Li ^{2,3
,
,}

1.
School of Biomedical Information and Engineering, Hainan Medical University, Haikou, China
2.
Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, China
3.
School of Mathematics and Statistics, Hainan Normal University, Haikou, China

Received: 20 August 2021 Revised: 28 November 2021 Accepted: 07 December 2021 Published: 15 December 2021
MSC : 11A07, 11B65, 33D15

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-analogue of a formula due to Liu ^[14].
- $ q $-supercongruence,
- basic hypergeometric series,
- creative microscoping method,
- Chinese remainder theorem for coprime polynomials
Citation: Chuanan Wei, Chun Li. New $ q $-supercongruences arising from a summation of basic hypergeometric series[J]. AIMS Mathematics, 2022, 7(3): 4125-4136. doi: 10.3934/math.2022228

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Abstract

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-analogue of a formula due to Liu ^[14].

References

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