Open Access
October, 2016 Identity families of multiple harmonic sums and multiple zeta star values
Jianqiang ZHAO
J. Math. Soc. Japan 68(4): 1669-1694 (October, 2016). DOI: 10.2969/jmsj/06841669


In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood, Hessami Pilehrood and Tauraso [Trans. Amer. Math. Soc. 366 (2014), pp.3131–3159]. As applications we prove several conjectures involving multiple zeta star values (MZSV): the Two-one formula conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al. involving 2-3-2-1 type MZSV, where the boldfaced 2 means some finite string of 2's.


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Jianqiang ZHAO. "Identity families of multiple harmonic sums and multiple zeta star values." J. Math. Soc. Japan 68 (4) 1669 - 1694, October, 2016.


Published: October, 2016
First available in Project Euclid: 24 October 2016

zbMATH: 1355.11089
MathSciNet: MR3564447
Digital Object Identifier: 10.2969/jmsj/06841669

Primary: 11M32
Secondary: 11B65 , 11B83

Keywords: binomial sums , multiple harmonic sums , multiple zeta star values , multiple zeta values , two-one formula

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 4 • October, 2016
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