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arXiv · 2511.00109

Further Classes of Series Involving Central Binomial Coefficients

Karl Dilcher·Christophe Vignat
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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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Karl Dilcher, Christophe Vignat. 2025-10-30. Further Classes of Series Involving Central Binomial Coefficients. https://arxiv.org/abs/2511.00109

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