A new class of the generalized Hermite-based polynomials

Abstract

The main object of this paper is to propose a new class of the Hermite-based polynomials by considering the Wiman (generalized Mittag-Leffler) function. We also indicate some analytical properties of our defined polynomials in a well-ordered way. Moreover, we consider a multi-index generalization of our generalized Hermite-based polynomials in the last section.