Identity Families of Multiple Harmonic Sums and Multiple Zeta (Star) Values

Abstract

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 et al. 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 2 means some finite string of 2's

22 pages, a new system of notation is used which greatly simplify the exposition of the paper

References in corpus (7)

• Quasi-shuffle products revisited
• The Bowman-Bradley theorem for multiple zeta-star values
• Congruences of alternating multiple harmonic sums
• On some combinations of multiple zeta-star values
• On $q$-analogues of two-one formulas for multiple harmonic sums and multiple zeta star values
• Note on relations among multiple zeta-star values
• Explicit evaluation of certain sums of multiple zeta-star values

Cited by in corpus (3)

• On $q$-Analogs of Some Families of Multiple Harmonic Sum and Multiple Zeta Star Value Identities
• Unramified Euler sums and Hoffman $\star$ basis
• On $q$-analogues of two-one formulas for multiple harmonic sums and multiple zeta star values