Explicit Identities and new results for Infinite Series associated with the Ratio of Central Binomial Coefficients

TL;DR

This paper derives new explicit identities and closed-form evaluations for infinite series involving ratios of central binomial coefficients, advancing the understanding of these mathematical series.

Contribution

It introduces novel explicit identities and closed-form formulas for infinite series related to ratios of central binomial coefficients, refining prior results.

Findings

New explicit identities for series involving binomial coefficient ratios

Closed-form evaluations of these infinite series

Refinement of previous results by Bhandari and Adegoke et al.

Abstract

We investigate some classes of infinite series involving central binomial coefficients, particularly focusing on those arising from ratios such as $\binom{2n}{n}\binom{4n}{2n}^{-1}$,$\binom{4n}{2n}\binom{2n}{n}^{-1}$ and related expressions. We derive several new explicit identities and closed-form evaluations, building on and refining previous results by Bhandari (2022) and Adegoke et al. (2022).