Hypergeometric evaluation identities and supercongruences

TL;DR

This paper uses hypergeometric evaluation identities to prove supercongruences, including a conjecture of van Hamme, advancing understanding of hypergeometric series and their valuations.

Contribution

It introduces new applications of hypergeometric evaluation identities to establish supercongruences, notably proving van Hamme's conjecture.

Findings

Proved several supercongruences related to hypergeometric series valuations.

Applied a strange valuation of Gosper to hypergeometric identities.

Confirmed van Hamme's conjecture on supercongruences.

Abstract

In this article, we provide an application of hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. In particular, we prove a conjecture of van Hamme.