Central Binomial Sums, Multiple Clausen Values and Zeta Values

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dc.creatorBorwein, J. M.
dc.creatorBroadhurst, D. J.
dc.creatorKamnitzer, J.
dc.date2000-04-22
dc.date.accessioned2026-07-07T04:09:47Z
dc.date.available2026-07-07T04:09:47Z
dc.descriptionWe find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.
dc.description17 pages, LaTeX, with use of amsmath and amssymb packages, to appear in Journal of Experimental Mathematics
dc.identifierhttps://arxiv.org/abs/hep-th/0004153
dc.identifierhttp://arxiv.org/abs/hep-th/0004153
dc.identifierExper.Math. 10 (2001) 25-34
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/49988
dc.subjectHigh Energy Physics - Theory
dc.subjectClassical Analysis and ODEs
dc.titleCentral Binomial Sums, Multiple Clausen Values and Zeta Values
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