Representations of \(\zeta (2n + 1)\) and related numbers in the form of definite integrals and rapidly convergent series

DOI10.1134/S1064562420050361zbMath1501.11087OpenAlexW3119702084MaRDI QIDQ2243795

Yanyan Li

Publication date: 11 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562420050361

zbMATH Keywords

Catalan's and Apéry's constantsintegral representation of series sumsvalues of Dirichlet beta function at even pointsvalues of Riemann zeta function at odd points

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Power series (including lacunary series) in one complex variable (30B10) Irrationality; linear independence over a field (11J72)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integral representations of the Riemann zeta function for odd-integer arguments
• Green's function of ordinary differential operators and an integral representation of sums of certain power series
• Integral representation of sums of series associated with special functions
• On integral representation of sums of some power series
• New rapidly convergent series representations for $\zeta (2n+1)$
• Irrationality of values of the Riemann zeta function
• Some definite integrals associated with the Riemann zeta function

This page was built for publication: Representations of \(\zeta (2n + 1)\) and related numbers in the form of definite integrals and rapidly convergent series