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October 13, 2025Notes on Number Theory and Discrete MathematicsOpen Access

Infinite series containing quotients of central binomial coefficients

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The work evaluates infinite series in closed form using Wallis' integral formula, indicating the relationship to pi.
Central binomial coefficients play a crucial role in the evaluation of these series, revealing connections to mathematical constants.
Integration by parts is utilized effectively to derive the results, emphasizing the importance of analytical techniques.
Findings indicate potential applications in advanced mathematical analysis and provide insights into series convergence.

Implication

This analysis evaluates infinite series using Wallis' integral and closed forms, highlighting pi and Riemann zeta function implications.

Abstract

By making use of the Wallis' integral formulae and integration by parts, two classes of infinite series are evaluated, in closed form, in terms of π and Riemann zeta function.

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Cite This Study

Zhiling Fan (2025) studied this question.

synapsesocial.com/papers/68ed3352c8c3d6f5ff5dd88c https://doi.org/10.7546/nntdm.2025.31.4.689-695

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Implication

This analysis evaluates infinite series using Wallis' integral and closed forms, highlighting pi and Riemann zeta function implications.

Abstract

By making use of the Wallis' integral formulae and integration by parts, two classes of infinite series are evaluated, in closed form, in terms of π and Riemann zeta function.

Infinite series containing quotients of central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

Infinite series containing quotients of central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

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