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A FAMILY OF MULTIPLE HARMONIC SUM AND MULTIPLE ZETA STAR VALUE IDENTITIES

Part of: Zeta and $L$-functions: analytic theory Sequences and sets

Published online by Cambridge University Press:  28 May 2014

Erin Linebarger  and
Jianqiang Zhao
Erin Linebarger
Affiliation:
Department of Mathematics, Eckerd College, St. Petersburg, FL 33711, U.S.A. email emlineba@eckerd.edu
Jianqiang Zhao
Affiliation:
Kavli Institute for Theoretical Physics China, Beijing, China Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany Department of Mathematics, Eckerd College, St. Petersburg, FL 33711, U.S.A. email zhaoj@eckerd.edu
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Abstract

In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al  [Trans. Amer. Math. Soc. (to appear)]. We then apply it to obtain a family of identities relating multiple zeta star values to alternating Euler sums. In such a typical identity the entries of the multiple zeta star values consist of blocks of arbitrarily long 2-strings separated by positive integers greater than two while the largest depth of the alternating Euler sums depends only on the number of 2-string blocks but not on their lengths.

MSC classification

Primary: 11B65: Binomial coefficients; factorials; $q$-identities 11M32: Multiple Dirichlet series and zeta functions and multizeta values

Information

Type
Research Article
Information
Mathematika , Volume 61 , Issue 1 , January 2015 , pp. 63 - 71
Copyright
Copyright © University College London 2014 

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