Laguerre-type general-Appell polynomials

Abstract

In this paper, new and general form of Laguerre-type Appell polynomials are introduced by using the Laguerre-type exponential function. For this new polynomial family, we present explicit representation, recurrence relation, lowering and raising operators, differential equation, determinant representation and some other properties. Furthermore, a method for handling matrix calculus-based approach to Laguerre-type general-Appell polynomials is presented. Finally, the special cases of this family are investigated using Hermite polynomials and truncated exponential-based Appell polynomials and their corresponding properties are obtained.