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2001 Central binomial sums, multiple Clausen values, and zeta values
Jonathan Michael Borwein, David J. Broadhurst, Joel Kamnitzer
Experiment. Math. 10(1): 25-34 (2001).

Abstract

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery 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 results involving polylogarithms in the golden ratio.

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Jonathan Michael Borwein. David J. Broadhurst. Joel Kamnitzer. "Central binomial sums, multiple Clausen values, and zeta values." Experiment. Math. 10 (1) 25 - 34, 2001.

Information

Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 0998.11045
MathSciNet: MR1 821 569

Subjects:
Primary: 11Mxx
Secondary: 05Axx , 11Bxx , 33Bxx

Keywords: Apéry sums , binomial sums , Clausen's function , log-sine integrals , multiple Clausen values , multiple zeta values , polylogarithms

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 1 • 2001
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