Vol. 9, No. 4, 2020

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

Doron Zeilberger and Wadim Zudilin

Vol. 9 (2020), No. 4, 407–419
Abstract

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

In memory of Naum Il'ich Feldman (1918–1994)

Keywords
$\pi$, irrationality measure, experimental mathematics, Almkvist–Zeilberger algorithm
Mathematical Subject Classification 2010
Primary: 11J82
Secondary: 11Y60, 33F10, 33C60
Milestones
Received: 13 December 2019
Revised: 7 January 2020
Accepted: 24 May 2020
Published: 5 November 2020
Authors
Doron Zeilberger
Department of Mathematics
Rutgers University–New Brunswick
Busch Campus
Piscataway, NJ
United States
Wadim Zudilin
Department of Mathematics
Institute for Mathematics, Astrophysics and Particle Physics
Radboud University
Nijmegen
Netherlands