Differential equation and recurrence relations of the Sheffer-Appell polynomial sequence: A matrix approach

Abstract

Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach, which we have used in this article, is convenient to derive the generating functions of the Sheffer-Appell polynomial sequence. By means of examples, we apply and also illustrate our results to an extended class of polynomial sequences.