An alternative proof of a theorem of Zagier

DOI10.1016/j.jmaa.2016.12.015zbMath1420.11119OpenAlexW2559783300MaRDI QIDQ504841

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood

Publication date: 17 January 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.12.015

zbMATH Keywords

residue theoremdigamma functionmultiple zeta valueEuler summultiple zeta star valuevery-well-poised hypergeometric series

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (5)

On harmonic numbers and nonlinear Euler sums ⋮ Generating functions for multiple zeta star values ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ Alternating double Euler sums, hypergeometric identities and a theorem of Zagier ⋮ Multiple zeta values and Euler sums

Cites Work

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• Mixed Tate motives over \(\mathbb{Z}\)
• Evaluation of the multiple zeta values \(\zeta(2,\ldots,2,3,2,\ldots,2)\)
• Multiple zeta values vs. multiple zeta-star values
• The algebra of multiple harmonic series
• An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series
• On \(q\)-analogs of some families of multiple harmonic sums and multiple zeta star value identities
• Another proof of Zagier's evaluation formula of the multiple zeta values \(\zeta (2, \dots , 2, 3, 2, \dots , 2)\)
• New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series

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