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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On an intriguing integral and some series related to $\zeta (4)$
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by David Borwein and Jonathan M. Borwein PDF
Proc. Amer. Math. Soc. 123 (1995), 1191-1198 Request permission

Abstract:

An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of $\pi \zeta (4),\zeta$ being the Riemann zeta function. From this we deduce by means of generating functions and Parseval’s identity the sums of certain series previously established by a completely different method.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1191-1198
  • MSC: Primary 11Y60; Secondary 11M06, 11Y35, 33B15, 42A16
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1231029-X
  • MathSciNet review: 1231029