On Poly-Euler Polynomials and Arakawa-Kaneko Type Zeta Functions of Parameters \(a,b,c\) - Acala, Nestor G.; Corcino, Roberto B. (Communications in Mathematics and Applications, 2021)
In this paper, we investigate a class of generalized poly-Euler polynomials with \(a,b,c\) parameters, a generalization of the classical Euler numbers and polynomials. Various properties of these generalized polynomials are established. We also introduce the Arakawa-Kaneko type zeta functions for the poly-Euler polynomials with \(a,b,c\) parameters and obtain an interpolation formula for the generalization of poly-Euler numbers and polynomials with \(a,b,c\) parameters. Furthermore, we establish the relationship between the Arakawa-Kaneko type zeta functions for generalized poly-Euler polynomials and the Arakawa-Kaneko zeta functions for generalized poly-Bernoulli polynomials defined in [1].