Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): David Borwein; 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.

References:

[1]: T. M. A. Apostol, Mathematical analysis, Second edition, Addison-Wesley, Cambridge, MA, 1975.
[2]: B. C. Berndt, Ramanujan's notebooks, Part I, Springer-Verlag, New York, 1985. MR 781125 (86c:01062)
[3]: R. B. Burckel, An introduction to classical complex analysis, Volume 1, Academic Press, New York, 1979. MR 555733 (81d:30001)
[4]: P. J. De Doelder, On some series containing $\psi (x) - \psi (y)$ and ${(\psi (x) - \psi (y))^2}$ for certain values of x and y, J. Comput. Appl. Math. 37 (1991), 125-141. MR 1136919 (92m:40002)
[5]: L. Lewin, Polylogarithms and associated functions, North-Holland, New York, 1981. MR 618278 (83b:33019)
[6]: K. R. Stromberg, An introduction to classical real analysis, Wadsworth, Belmont, CA, 1981. MR 604364 (82c:26002)
[7]: A. J. van der Poorten, Some wonderful formulae...An introduction to polylogarithms, Proceedings of Number Theory Conference, Kingston, Ontario, 1979, pp. 269-286. MR 634694 (83b:10043)

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