The irrationality measure of $\pi$ is at most $7.103205334137\dots$

Doron Zeilberger; Wadim Zudilin

doi:10.2140/moscow.2020.9.407

Abstract

We use a variant of Salikhov’s ingenious proof that the irrationality measure of $π$ is at most $7.606308 \dots$ to prove that, in fact, it is at most $7.103205334137 \dots$ .

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Doron Zeilberger. Wadim Zudilin. "The irrationality measure of $\pi$ is at most $7.103205334137\dots$." Mosc. J. Comb. Number Theory 9 (4) 407 - 419, 2020. https://doi.org/10.2140/moscow.2020.9.407

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Received: 13 December 2019; Revised: 7 January 2020; Accepted: 24 May 2020; Published: 2020

First available in Project Euclid: 12 November 2020

zbMATH: 07272358

MathSciNet: MR4170705

Digital Object Identifier: 10.2140/moscow.2020.9.407

Subjects:

Primary: 11J82

Secondary: 11Y60 , 33C60 , 33F10

Keywords: $\pi$ , Almkvist–Zeilberger algorithm , experimental mathematics , irrationality measure

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