Infinite series containing quotients of central binomial coefficients | Synapse
October 13, 2025Open Access
Infinite series containing quotients of central binomial coefficients
Key Points
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.
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 and Riemann zeta function.