Values of the Riemann zeta function and the Dirichlet beta function at positive integer points and multiple numerical series

DOI10.1134/S0001434622110396OpenAlexW4313365182MaRDI QIDQ2680758

Yanyan Li

Publication date: 4 January 2023

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434622110396

zbMATH Keywords

multiple numerical seriesMordell-Tornheim seriesvalues of Riemann zeta function and Dirichlet beta function at positive integer points

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41)

Uses Software

• DLMF

Cites Work

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• Derivatives and fast evaluation of the Tornheim zeta function
• Some new identities for \(\zeta(k)\).
• Green's function of ordinary differential operators and an integral representation of sums of certain power series
• On the Evaluation of Some Multiple Series
• Hilbert's Inequality and Witten's Zeta-Function
• An Elementary Proof of ∑ ∞ n = 1 1/n 2 = π 2 /6
• Euler Sums and Contour Integral Representations
• Ordinary differential operators and the integral representation of sums of certain power series
• Harmonic Double Series

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