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Recently, the level two analogue of multiple polylogarithm function ${\rmA}(k_1,\ldots,k_r;z)$ and Arakawa-Kaneko zeta function $\psi(k_1,\ldots,k_r;s)$were introduced by M. Kaneko and H. Tsumura, for $k_1,\ldots,k_r \in\mathbb{Z}_{\ge 1}$ . In this paper, we investigate some of their specialrelations. In particular, we prove some explicit forms of ${\rmA}(k_1,\ldots,k_r;z)$ and $\psi(k_1,\ldots,k_r;s)$. Also, we introduce a level$m$ anlogue of the Arakawa-Kaneko zeta functions.

Some results on Arakawa-Kaneko, Kaneko-Tsumura functions and related functions