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Multiple zeta-star values and multiple integrals. (English) Zbl 1421.11069

Summary: We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class includes both multiple zeta and zeta-star values of Euler-Zagier type, and also several other types of multiple zeta values. We show that these integrals can be used to obtain some relations among such zeta values quite transparently.

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
40B05 Multiple sequences and series
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