Some series representations of \(\zeta(2n+1)\)

DOI10.1216/rmjm/1181072507zbMath0808.11053OpenAlexW2083525849MaRDI QIDQ1328252

Kenneth S. Williams, Nan-Yue Zhang

Publication date: 27 February 1995

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072507

zbMATH Keywords

Riemann zeta-functionseries representations for \(\zeta(3)\)Epstein-Hurwitz zeta functionexpansion of derivativeszeta function at odd integers

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Special sequences and polynomials (11B83) Hurwitz and Lerch zeta functions (11M35)

Related Items

Some families of series representations for the Riemann \(\zeta(3)\), Further series representations for \(\zeta(2n+1)\), Two series which generalize Dirichlet’s lambda and Riemann’s zeta functions at positive integer arguments, Certain classes of series associated with the Zeta and related functions., New rapidly convergent series representations for $\zeta (2n+1)$, Some definite integrals associated with the Riemann zeta function, Special issue: Higher transcendental functions and their applications, A certain class of rapidly convergent series representations for \(\zeta (2n + 1)\), Some simple algorithms for the evaluations and representations of the Riemann zeta function at positive integer arguments, Computational strategies for the Riemann zeta function, Unnamed Item

Cites Work

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• On Values of the Riemann Zeta Function at Integral Arguments
• An Asymptotic Expansion for the First Derivative of the Generalized Riemann Zeta Function
• An Elementary Proof of ∑ ∞ n = 1 1/n 2 = π 2 /6
• A New Series Representation for ζ(3)
• Computation of certain functions related to the Hurwitz zeta-function
• Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals