Further Classes of Series Involving Central Binomial Coefficients

2025/10/30 by Karl Dilcher, Dilcher, Karl, Christophe Vignat +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2511.00109

openalex publication_date 2025/10/30 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28

Abstract

Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including exponential Bell polynomials and integral representations, to further extend these results. Throughout the paper, we make extensive use of the gamma and polygamma functions and their properties.

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