Alternating multiple zeta values, and explicit formulas of some Euler–Apéry-type series. (March 2021)

• Record Type: Journal Article
• Authors: Wang, Weiping; Xu, Ce
• Is Part Of: European journal of combinatorics. Volume 93(2021)
• Publication Date: 2021-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2020.103283
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: In this paper, we study some Euler–Apéry-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and alternating multiple zeta values. Based on these formulas, we further show that some other series are reducible to ln ( 2 ), zeta values, and alternating multiple zeta values by considering the contour integrals related to gamma function, polygamma function and trigonometric functions. The evaluations of a large number of special Euler–Apéry-type series are presented as examples.