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This article is available for purchase or by subscription. See below.
Abstract
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We prove two integral transformations that relate different constructions of rational approximations
to .
The first one relates a double integral over the unit square and a Barnes-type
integral. The second one relates two Barnes-type integrals and was discovered and
proved by W. Zudilin using an automated proof method. Here we offer a proof based
on more classical means such as contiguous relations, the second Barnes lemma and
the duplication formula for the gamma function.
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To the memory of Naum Ilyitch Feldman
(1918–1994)
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Keywords
Legendre polynomials, irrationality measure, zeta values,
hypergeometric functions, human-generated proofs
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Mathematical Subject Classification 2010
Primary: 11J82
Secondary: 33C20, 33C60
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Milestones
Received: 31 December 2019
Accepted: 5 May 2020
Published: 5 November 2020
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