A new generalization of Laguerre-based Appell polynomials

Abstract

In this paper we define a new generalization of Laguerre-based Appel polynomials. We obtain recurrence relation, lowering operator, integro partial raising operator, integro partial differential equation and determinant representation for this new polynomial family. We introduce subpolynomials of these polynomials, namely Laguerre-based-Hermite Frobenius Euler polynomials and Laguerre based MillerLee polynomials, and obtain various properties of them. We also show 3D graphs of these subfamilies and graphs of the distribution of their zeros.