A simpler proof of a Katsurada's theorem and rapidly converging series for \(\zeta (2n+1)\) and \(\beta (2n)\)

DOI10.1007/S10231-014-0409-3zbMath1393.11059arXiv1203.5660OpenAlexW3098300471MaRDI QIDQ2353828

Fábio M. S. Lima

Publication date: 9 July 2015

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5660

zbMATH Keywords

Riemann zeta functionClausen functionzeta seriesDirichlet beta function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) (zeta (s)) and (L(s, chi)) (11M06) Algorithms for approximation of functions (65D15) Dirichlet series, exponential series and other series in one complex variable (30B50)

Related Items (3)

The Euler-Riemann zeta function in some series formulae and its values at odd integer points ⋮ Renewal sequences and record chains related to multiple zeta sums ⋮ Numerical calculation of the Riemann zeta function at odd-integer arguments: a direct formula method

Uses Software

• DLMF

Cites Work

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• An Euler-type formula for \(\xi (2k+1)\)
• Further series representations for \(\zeta(2n+1)\)
• A certain class of rapidly convergent series representations for \(\zeta (2n + 1)\)
• Computational strategies for the Riemann zeta function
• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• Another proof of Euler’s formula for $\zeta(2k)$
• An Euler-type formula forβ(2n) and closed-form expressions for a class of zeta series
• Rapidly convergent series representations for ζ(2n+1) and their χ-analogue

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