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2013 Algorithms for Some Euler-Type Identities for Multiple Zeta Values
Shifeng Ding, Weijun Liu
J. Appl. Math. 2013(none): 1-7 (2013). DOI: 10.1155/2013/802791

Abstract

Multiple zeta values are the numbers defined by the convergent series ζ(s1,s2,,sk)=n1>n2>>nk>0(1/n1s1n2s2nksk), where s1, s2, , sk are positive integers with s1>1. For kn, let E(2n,k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n,2)=3ζ(2n)/4 was extended to E(2n,3) and E(2n,4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n,k) and then gave a direct formula for E(2n,k) for arbitrary kn. In this paper we apply a technique introduced by Granville to present an algorithm to calculate E(2n,k) and prove that the direct formula can also be deduced from Eisenstein's double product.

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Shifeng Ding. Weijun Liu. "Algorithms for Some Euler-Type Identities for Multiple Zeta Values." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/802791

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.11092
MathSciNet: MR3032190
Digital Object Identifier: 10.1155/2013/802791

Rights: Copyright © 2013 Hindawi

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