Supercongruences related to ${}_3F_2(1)$ involving harmonic numbers

TL;DR

This paper investigates supercongruences involving truncated hypergeometric series with harmonic numbers, providing new congruence relations and evaluating related infinite series.

Contribution

It introduces new supercongruences for ${}_3F_2(1)$ series involving harmonic numbers and evaluates their corresponding infinite series.

Findings

Established new supercongruences for truncated hypergeometric series.

Evaluated related infinite series explicitly.

Connected supercongruences with harmonic number properties.

Abstract

We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.