On functions of Arakawa and Kaneko and multiple zeta functions

Markus Kuba

We study for $s\in \mathbb{N}=\{1,2,...\}$ the functions $ξ_{k}(s)=\frac{1}{Γ(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k}(1-e^{-t})dt$, and more generally $ξ_{k_1,...,k_r}(s)=\frac{1}{…