Vol. 9, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
Author Index
To Appear
Other MSP Journals
Two integral transformations related to $\zeta(2)$

Raffaele Marcovecchio

Vol. 9 (2020), No. 4, 441–452

We prove two integral transformations that relate different constructions of rational approximations to ζ(2). 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.

To the memory of Naum Ilyitch Feldman (1918–1994)

Legendre polynomials, irrationality measure, zeta values, hypergeometric functions, human-generated proofs
Mathematical Subject Classification 2010
Primary: 11J82
Secondary: 33C20, 33C60
Received: 31 December 2019
Accepted: 5 May 2020
Published: 5 November 2020
Raffaele Marcovecchio