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arXiv · 2505.04395

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

Chen Wang·Yu-Chan Tian·Kai Huang
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Abstract

In 1997, Van Hamme proposed 13 supercongruences corresponding to $1/\pi$ 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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Chen Wang, Yu-Chan Tian, Kai Huang. 2025-05-07. A refined $q$-analogue of some congruences of Van Hamme. https://arxiv.org/abs/2505.04395

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