A unified matrix approach to the Legendre–Sheffer and certain hybrid polynomial sequences

The aim of this article is to study certain properties of the Legendre–Sheffer polynomials by making effective use of matrix algebra. The recursive formulas and differential equation for the Legendre–Sheffer polynomials are established by using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Legendre-associated Sheffer and Legendre–Appell families are derived. Moreover, certain examples of these polynomials are also considered which serve as a focal theme of the study. This approach provides a powerful tool for investigating the properties of the hybrid polynomial sequences.