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

Segun Olofin Akerele, Yao Mawugna Dzokotoe

Published 2025-05-02Version 1

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).