# Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Apéry

@article{DoughertyBliss2022TweakingTB,
title={Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Ap{\'e}ry},
author={Robert Dougherty-Bliss and Christoph Koutschan and Doron Zeilberger},
journal={The Ramanujan Journal},
year={2022}
}
• Published 20 January 2021
• Philosophy, Computer Science
• The Ramanujan Journal
As we all know, he was proven wrong by Gödel and Turing in general, but even for such concrete problems, like the irrationality of a specific, natural, constant, like the Euler-Mascheroni constant (that may be defined in terms of the definite integral − ∞ 0 e−x log x) , that is most probably decidable in the logical sense, (i.e. there probably exists a (rigorous) proof), we lowly humans did not yet find it, (and may never will!).
Exploring General Apéry Limits via the Zudilin-Straub t-transform
• Mathematics
ArXiv
• 2022
Abstract: Inspired by a recent beautiful construction of Armin Straub and Wadim Zudilin, that ‘tweaked’ the sum of the s powers of the n-th row of Pascal’s triangle, getting instead of sequences of
The birthday boy problem
In their recent (2021) preprint, Robert Dougherty-Bliss, Christoph Koutschan and Doron Zeilberger come up with a powerful strategy to prove the irrationality, in a quantitative form, of some numbers
Integral Recurrences from A to Z
George Boros and Victor Moll’s masterpiece Irresistible Integrals does well to include a suitably-titled appendix, “The Revolutionary WZ Method,” which gives a brief overview of the celebrated
Experimenting with Apéry Limits and WZ pairs
• Mathematics
Maple Transactions
• 2021
This article, dedicated with admiration in memory of Jon and Peter Borwein,illustrates by example, the power of experimental mathematics, so dear to them both, by experimenting with so-called Apéry
APÉRY LIMITS FOR ELLIPTIC -VALUES
• Mathematics
Bulletin of the Australian Mathematical Society
• 2022
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In their recent (2021) preprint, Robert Dougherty-Bliss, Christoph Koutschan and Doron Zeilberger come up with a powerful strategy to prove the irrationality, in a quantitative form, of some numbers
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© Séminaire Delange-Pisot-Poitou. Théorie des nombres (Secrétariat mathématique, Paris), 1978-1979, tous droits réservés. L’accès aux archives de la collection « Séminaire Delange-Pisot-Poitou.
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