Central binomial sums, multiple Clausen values, and zeta valuse

Borwein, Jonathan Michael; Broadhurst, David J. and Kamnitzer, Joel (2001). Central binomial sums, multiple Clausen values, and zeta valuse. Experimental Mathematics, 10(1) pp. 25–34.

DOI: https://doi.org/10.1080/10586458.2001.10504426

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 nonalternating 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 resuIts involving polylogarithms in the golden ratio.

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