An extension of a supercongruence of Long and Ramakrishna

TL;DR

This paper proves two supercongruences for truncated hypergeometric series, extending a recent result by Long and Ramakrishna through hypergeometric identities like Whipple's transformation.

Contribution

It introduces an uniparametric extension of a supercongruence, advancing the understanding of hypergeometric series supercongruences.

Findings

Proved two new supercongruences for specific hypergeometric series.

Extended a recent supercongruence result by Long and Ramakrishna.

Utilized hypergeometric identities such as Whipple's transformation in proofs.

Abstract

We prove two supercongruences for specific truncated hypergeometric series. These include an uniparametric extension of a supercongruence that was recently established by Long and Ramakrishna. Our proofs involve special instances of various hypergeometric identities including Whipple's transformation and the Karlsson--Minton summation.