A refined $q$-analogue of some congruences of Van Hamme

Fuente: arXiv
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Main Authors: Wang, Chen, Tian, Yu-Chan, Huang, Kai
Format: Preprint
Published: 2025
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author Wang, Chen
Tian, Yu-Chan
Huang, Kai
author_facet Wang, Chen
Tian, Yu-Chan
Huang, Kai
contents In 1997, Van Hamme proposed 13 supercongruences corresponding to $1/π$ series of the Ramanujan-type. Inspired by the recent work of V.J.W. Guo, we establish a unified $q$-analogue of Van Hamme's (B.2), (E.2) and (F.2) supercongruences, which is also a refinement of some known results obtained by different authors. As a consequence, we give a parametric supercongruence related to the Euler polynomials.
format Preprint
id arxiv_https___arxiv_org_abs_2505_04395
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A refined $q$-analogue of some congruences of Van Hamme
Wang, Chen
Tian, Yu-Chan
Huang, Kai
Number Theory
Combinatorics
In 1997, Van Hamme proposed 13 supercongruences corresponding to $1/π$ series of the Ramanujan-type. Inspired by the recent work of V.J.W. Guo, we establish a unified $q$-analogue of Van Hamme's (B.2), (E.2) and (F.2) supercongruences, which is also a refinement of some known results obtained by different authors. As a consequence, we give a parametric supercongruence related to the Euler polynomials.
title A refined $q$-analogue of some congruences of Van Hamme
topic Number Theory
Combinatorics
url https://arxiv.org/abs/2505.04395