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

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)

$\pi$, irrationality measure, experimental mathematics, Almkvist–Zeilberger algorithm
Mathematical Subject Classification 2010
Primary: 11J82
Secondary: 11Y60, 33F10, 33C60
Received: 13 December 2019
Revised: 7 January 2020
Accepted: 24 May 2020
Published: 5 November 2020
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