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On an intriguing integral and some series related to ζ (4)

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posted on 2025-05-10, 08:18 authored by David Borwein, Jonathan M. Borwein
An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of πζ (4), ζ 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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Related Materials

  1. 1.
    DOI - Is published in https://doi.org/10.1090/S0002-9939-1995-1231029-X
  2. 2.
    ISSN - Is version of https://portal.issn.org/resource/ISSN/0002-9939

Journal title

Proceedings of the American Mathematical Society

Volume

123

Issue

4

Pagination

1191-1198

Publisher

American Mathematical Society (AMS)

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

Rights statement

First published in Proceedings of the American Mathematical Society in Vol. 123, No. 4, pp. 1191-1198, 1995 published by the American Mathematical Society.

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    Keywords

    Riemann zeta functionParseval's identitygenerating functionslog-cosine integralspolylogarithms

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