A new generalization of Laguerre-based Appell polynomials with two parameters

Abstract

In this paper, we define a new generalization of Laguerre-based Appell polynomials with two parameters. We obtain a recurrence relation, a lowering operator, a integro-partial raising operator, a integro-partial differential equation for this new polynomial family. We introduce subpolynomials of these polynomials, namely Laguerre-based Hermite-Frobenius Euler polynomials, Laguerre-based Miller-Lee polynomials and generalizations of Laguerre-based Hermite polynomials and obtain various properties of them. We also show 3D graphs of these subfamilies and graphs of the distribution of their real roots.