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Explicit Identities and new results for Infinite Series associated with the Ratio of Central Binomial Coefficients (2505.09632v1)
Published 2 May 2025 in math.NT and math.CO
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).
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