Approximations to di- and tri-logarithms

DOI10.1016/j.cam.2005.04.076zbMath1220.65028arXivmath/0409023OpenAlexW1986956324MaRDI QIDQ875388

Wadim Zudilin

Publication date: 13 April 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409023

zbMATH Keywords

dilogarithmpolylogarithmhypergeometric serieszeta functiontrilogarithmApéry approximation

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Computation of special functions and constants, construction of tables (65D20) Continued fractions and generalizations (11J70) Generalized hypergeometric series, ({}_pF_q) (33C20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

Moduli spaces and modular forms. Abstracts from the workshop held January 31 -- February 6, 2021 (hybrid meeting) ⋮ Multiple Legendre polynomials in diophantine approximation ⋮ Apéry limits and special values of \(L\)-functions ⋮ Two integral transformations related to \(\zeta (2)\) ⋮ Apéry Limits: Experiments and Proofs ⋮ On simultaneous Diophantine approximations to \(\zeta(2)\) and \(\zeta(3)\) ⋮ Two hypergeometric tales and a new irrationality measure of \(\zeta (2)\) ⋮ Unnamed Item

Cites Work

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• Integral identities and constructions of approximations to zeta-values
• On the linear independence of the values of polylogarithmic functions
• Padé approximations to the generalized hypergeometric functions. I
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• A third-order Apéry-like recursion for \(\zeta(5)\)
• A Note on the Irrationality of ζ(2) and ζ(3)
• Rational Approximations to the Dilogarithm
• Irrationality of infinitely many values of the zeta function at odd integers.

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