Automatic discovery of irrationality proofs and irrationality measures

DOI10.1142/S1793042120400230zbMath1468.11160arXiv1912.10381OpenAlexW3104368852WikidataQ113776666 ScholiaQ113776666MaRDI QIDQ4991708

Wadim Zudilin, Doron Zeilberger

Publication date: 3 June 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10381

zbMATH Keywords

experimental mathematicsirrationality measure exponentAlmkvist-Zeilberger algorithmWilf-Zeilberger algorithmic proof theorylinear independence measure exponent

Mathematics Subject Classification ID

Measures of irrationality and of transcendence (11J82) Distribution modulo one (11J71) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (2)

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

Uses Software

• MultiZeilberger
• DEtools

Cites Work

• The method of differentiating under the integral sign
• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• On the irrationality measure of \(\ln 3\)
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Linear independence of 1, \(\operatorname{Li}_1\) and \(\operatorname{Li}_2\)
• The Rhin–Viola method for log 2
• Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
• A Note on the Irrationality of ζ(2) and ζ(3)
• The irrationality of $\log (1+1/q) \log (1-1/q)$
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