Abstract
We establish some supercongruences for the truncated $_{2}F_{1}$ and $_{3}F_{2}$ hypergeometric series involving the $p$-adic gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated $_{3}F_{2}$ hypergeometric series. Related supercongruences modulo $p^{3}$ are proposed as conjectures.
Publisher
Cambridge University Press (CUP)
Cited by
6 articles.
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1. Supercongruences involving products of three binomial coefficients;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-06-13
2. On two congruence conjectures of Z.-W. Sun involving Franel numbers;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2023-05-16
3. A local-global theorem for p-adic supercongruences;Journal für die reine und angewandte Mathematik (Crelles Journal);2022-07-23
4. Some q-analogues of supercongruences for truncated $$_3F_2$$ hypergeometric series;The Ramanujan Journal;2021-08-10
5. On two congruences involving Franel numbers;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2020-09-13