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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On an intriguing integral and some series related to $ \zeta(4)$


Authors: David Borwein and Jonathan M. Borwein
Journal: Proc. Amer. Math. Soc. 123 (1995), 1191-1198
MSC: Primary 11Y60; Secondary 11M06, 11Y35, 33B15, 42A16
MathSciNet review: 1231029
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1231029-X
PII: S 0002-9939(1995)1231029-X
Keywords: Riemann zeta function, Parseval's identity, generating functions, log-cosine integrals, polylogarithms
Article copyright: © Copyright 1995 American Mathematical Society