The p-adic Arakawa–Kaneko–Hamahata zeta functions and poly-Euler polynomials

In this paper, we give a definition of the p-adic Arakawa–Kaneko–Hamahata zeta functions. These zeta functions interpolate Hamahata's poly-Euler polynomials at non-positive integers. We prove the derivative formula, the difference equation and the reflection formula of these zeta functions. Furthermore, we also prove a sums of products identity and a closed form of Hamahata's poly-Euler polynomials in terms of the Stirling numbers of the second kind.