On functions of Arakawa and Kaneko and multiple zeta functions

Details On functions of Arakawa and Kaneko and multiple zeta functions On functions of Arakawa and Kaneko and multiple zeta functions

2009-03-26

arxiv.org/abs/0903.4552v1

Mathematics

Number Theory

5 pages

Scientific paper

We study for $s\in\N=\{1,2,...\}$ the functions $\xi_{k}(s)=\frac{1}{\Gamma(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k}(1-e^{-t})dt$, and more generally $\xi_{k_1,...,k_r}(s)=\frac{1}{\Gamma(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k_1,...,k_r}(1-e^{-t})dt$, introduced by Arakawa and Kaneko \cite{Arakawa} and relate them with (finite) multiple zeta functions, partially answering a question of \cite{Arakawa}. In particular, we give an alternative proof of a result of Ohno \cite{Ohno2}.

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