Evaluations of some Euler-Apéry-type series

DOI10.1007/s13226-021-00191-9OpenAlexW3203624579MaRDI QIDQ2095055

Ying Li, Yu-Jie Wang, Ce Xu

Publication date: 9 November 2022

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-021-00191-9

zbMATH Keywords

generating functioncontour integrationFuss-Catalan numbersEuler-Apéry-type series

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Uses Software

• MultipleZetaValues

Cites Work

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• Multivariate Fuss-Catalan numbers
• Catalan numbers, their generalization, and their uses
• Multiple harmonic series
• Identities for the multiple zeta (star) values
• Explicit relations between multiple zeta values and related variants
• Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series
• Analytic continuation of multiple polylogarithms
• Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values
• Interesting Series Involving the Central Binomial Coefficient
• Iterated path integrals
• Euler Sums and Contour Integral Representations
• Generalized Arakawa-Kaneko zeta functions
• Algebras of Iterated Path Integrals and Fundamental Groups

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