Some definite integrals associated with the Riemann zeta function

DOI10.4171/ZAA/982zbMath0979.11042MaRDI QIDQ5926117

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Publication date: 24 February 2002

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/49048

zbMATH Keywords

Riemann zeta functionpositive odd integer valuesseries representationstrigonometric integrals

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (14)

An Euler-type formula forβ(2n) and closed-form expressions for a class of zeta series ⋮ Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results ⋮ Series representations for the Apéry constant \(\zeta (3)\) involving the values \(\zeta (2n)\) ⋮ On the condition number of Newton interpolation: Chebyshev points and monotonically ordering ⋮ Certain classes of series associated with the Zeta and related functions. ⋮ Rapidly converging series for \(\zeta(2 n + 1)\) from Fourier series ⋮ A massive Feynman integral and some reduction relations for Appell functions ⋮ Representations of \(\zeta (2n + 1)\) and related numbers in the form of definite integrals and rapidly convergent series ⋮ Evaluations of some classes of the trigonometric moment integrals ⋮ Explicit evaluations of some families of log-sine and log-cosine integrals ⋮ On values of the Riemann zeta function at positive integers ⋮ Closed-form evaluations of definite integrals and associated infinite series involving the Riemann zeta function ⋮ Multiple gamma and related functions ⋮ Unnamed Item

Cites Work

• Some families of series representations for the Riemann \(\zeta(3)\)
• Further series representations for \(\zeta(2n+1)\)
• Some series representations of \(\zeta(2n+1)\)
• Computational strategies for the Riemann zeta function
• On the zeta function values \(\zeta (2k+1)\), \(k=1, 2, \dots\)
• Nielsen’s Generalized Polylogarithms
• A New Series Representation for ζ(3)
• Euler and the Zeta Function
• Some rapidly converging series for $\zeta (2n+1)$
• Some series of the zeta and related functions
• New rapidly convergent series representations for $\zeta (2n+1)$
• Notes on Riemann's ζ-Function
• Some Integrals of the Arctangent Function
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