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October 16, 2025Open Access

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

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New closed-form evaluations for infinite series linked to central binomial coefficients were derived.
The investigation refines previous results, showcasing explicit identities for specific ratios of coefficients.
Focus was on the classes of series derived from ratios like $inom{2n}{n}inom{4n}{2n}^{-1}$ and related forms.
Findings build upon earlier work by Bhandari and Adegoke, indicating a progression in understanding these coefficients.

Implication

Research investigates infinite series ratios of central binomial coefficients, highlighting new identities.

Abstract

We investigate some classes of infinite series involving central binomial coefficients, particularly focusing on those arising from ratios such as 2nn4n2n⁻¹,4n2n2nn⁻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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Cite This Study

Dzokotoe et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd0f6 https://doi.org/10.48550/arxiv.2505.09632

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Implication

Research investigates infinite series ratios of central binomial coefficients, highlighting new identities.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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