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A refined q-analogue of some congruences of Van Hamme

2025/05/07 by Wang, Chen, Tian, Yu-Chan, Huang, Kai
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.04395

Abstract

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.

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