Series with harmonic-like numbers and squared binomial coefficients

Xiaoyuan Wang; Wenchang Chu

doi:10.1216/rmj.2022.52.1849

Abstract

By reformulating the Gauss summation theorem with a free variable $x$ so that both sides of the equality can be expanded into Maclaurin series, we evaluate, in closed form, many different infinite series containing harmonic-like numbers and squared central binomial coefficients.

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Xiaoyuan Wang. Wenchang Chu. "Series with harmonic-like numbers and squared binomial coefficients." Rocky Mountain J. Math. 52 (5) 1849 - 1866, October 2022. https://doi.org/10.1216/rmj.2022.52.1849

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Received: 16 February 2021; Revised: 31 October 2021; Accepted: 19 January 2022; Published: October 2022

First available in Project Euclid: 28 November 2022

MathSciNet: MR4563756

zbMATH: 1510.11072

Digital Object Identifier: 10.1216/rmj.2022.52.1849

Subjects:

Primary: 05A19

Secondary: 33C20 , 65B10

Keywords: central binomial coefficient , Gauss summation theorem , harmonic numbers , hypergeometric series , Ramanujan-like series , the Γ-function

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