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Central Binomial Sums, Multiple Clausen Values and Zeta Values

Borwein, Jonathan M. and Broadhurst, David J. and Kamnitzer, Joel (2001) Central Binomial Sums, Multiple Clausen Values and Zeta Values. Experimental Mathematics, 10 (1). pp. 25-41.

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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 Ap\'ery sums). The study of on-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.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: binomial sums, multiple zeta values, log-sine integrals, Clausens function, multiple Clausen values, polylogarithms, Apery sums
      Subjects: 11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory
      40-xx Sequences, series, summability > 40Bxx Multiple sequences and series
      33-xx Special functions > 33Exx Other special functions
      11-xx Number theory > 11Yxx Computational number theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 13 Jan 2015 12:24
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/243

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