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On functions of Arakawa and Kaneko and multiple zeta functions. (English) Zbl 1299.11064
Author’s abstract: We study two functions $$\xi_k(s)$$ and $$\xi_{k_1,\dots,k_r}(s)$$ introduced by T. Arakawa and M. Kaneko [Nagoya Math. J. 153, 189–209 (1999; Zbl 0932.11055)] and relate them with (finite) multiple zeta values and multiple zeta star values using elementary methods. In particular, we give an alternative proof of a result of Y. Ohno [J. Number Theory 74, 39–43 (1999; Zbl 0920.11063)].

##### MSC:
 11M32 Multiple Dirichlet series and zeta functions and multizeta values
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