# 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} }

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!).

## 5 Citations

Exploring General Apéry Limits via the Zudilin-Straub t-transform

- MathematicsArXiv
- 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

- Mathematics
- 2021

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

- Geology
- 2021

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

- MathematicsMaple 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

- MathematicsBulletin of the Australian Mathematical Society
- 2022

<jats:p>For an (irreducible) recurrence equation with coefficients from <jats:inline-formula>
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<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink"…

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The birthday boy problem

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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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