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Central Binomial Sums, Multiple Clausen Values and Zeta Values

J. M. Borwein·D. J. Broadhurst·J. Kamnitzer
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Abstract

We 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.

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J. M. Borwein, D. J. Broadhurst, J. Kamnitzer. 2000-04-22. Central Binomial Sums, Multiple Clausen Values and Zeta Values. https://arxiv.org/abs/hep-th/0004153

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