THE UMBRAL-ALGEBRAIC APPROACH TO STUDY THE SHEFFER-λ POLYNOMIALS

Abstract

In this article, the family of Sheffer-associated λ polynomials is introduced, and their quasi-monomial properties are established. Additionally, certain properties of these polynomials are explored using umbral algebraic matrix algebra. This approach provides a powerful tool for investigating the properties of multi-variable special polynomials. The recursive formulae and differential equations for these polynomials are derived using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Appellassociated λ polynomials and Appell-λ polynomial families are also obtained. Furthermore, these findings are demonstrated for the Hermite-λ, exponential-λ, and Miller-Lee-λ polynomials.