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arXiv · 1507.07391

Supercongruences for truncated hypergeometric series and p-adic gamma function

Rupam Barman·Neelam Saikia
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Abstract

We prove three more general supercongruences between truncated hypergeometric series and $p$-adic Gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson using the theory of finite field hypergeometric series follows from one of our more general supercongruences. We also prove a supercongruence for ${_7}F_6$ truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.

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Rupam Barman, Neelam Saikia. 2015-07-27. Supercongruences for truncated hypergeometric series and p-adic gamma function. https://arxiv.org/abs/1507.07391

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