Apéry Limits: Experiments and Proofs

DOI10.1080/00029890.2021.1962153zbMath1498.11045arXiv2011.03400OpenAlexW3212107819WikidataQ113853670 ScholiaQ113853670MaRDI QIDQ5163936

Armin Straub, Marc Chamberland

Publication date: 9 November 2021

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.03400

Mathematics Subject Classification ID

Recurrences (11B37) Continued fractions (11A55) Special sequences and polynomials (11B83)

Related Items (3)

Exploring general Apéry limits via the Zudilin–Straub t-transform ⋮ Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Apéry ⋮ APÉRY LIMITS FOR ELLIPTIC -VALUES

Cites Work

• Arithmetic of linear forms involving odd zeta values
• Some recurrences for sums of powers of binomial coefficients
• Apéry's double sum is plain sailing indeed
• Approximations to di- and tri-logarithms
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• \(q\)-Apéry irrationality proofs by \(q\)-WZ pairs
• Bounds for the length of recurrence relations for convolutions of P-recursive sequences
• Irrationality proofs for zeta values, moduli spaces and dinner parties
• Apéry limits and special values of \(L\)-functions
• A Note on the Irrationality of ζ(2) and ζ(3)
• Neverending Fractions
• Continued Fractions of Tails of Hypergeometric Series
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