Some parametric 𝑞-supercongruences from a summation of Gasper and Rahman

He, Haihong; Wang, Xiaoxia

doi:10.1090/proc/16923

Some parametric $q$-supercongruences from a summation of Gasper and Rahman
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by Haihong He and Xiaoxia Wang;

Proc. Amer. Math. Soc. 152 (2024), 4775-4784

DOI: https://doi.org/10.1090/proc/16923

Published electronically: September 24, 2024

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Abstract:

By employing a quadratic summation formula due to Gasper and Rahman [Basic hypergeometric series, 2nd ed, vol. 96, Cambridge University Press, Cambridge, 2004] and the creative microscoping method developed by Guo and Zudilin [Adv. Math. 346 (2019), pp. 329–358], we establish some new parametric $q$-supercongruences, the corresponding supercongruences of which can be deemed the variants of Van Hamme’s (J.2) and (L.2) supercongruences. Moreover, we obtain three families of Ramanujan-type formulas on $\pi$ and propose a challenging conjecture.

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