Accelerating the Hypergeometric Function with the Beta Integral to Derive New Infinite Series for π and Values of the Gamma Function

2024/02/12 by Hakimoglu, Cetin · 1 citation
#11Y60 #40A25 (Primary) 11B65 #65B10 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.08693

Abstract

The beta integral is applied to accelerate the hypergeometric function 2 F 1\1, B; C ; w\ to derive new infinite series for constants such as π and values of the gamma function. A compendium of new infinite series is given. Ramanujan-like formulas for pi are also derived based on elementary inverse trigonometric functions, including a formula with rational values that adds 2.5 digits per terms, which makes the series much more compact than similar formulas in the existing literature.

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• Analytic Dilogarithm Identities

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