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

## TL;DR

This paper uses matrix algebra to derive identities, differential equations, and generating functions for Sheffer-Appell polynomial sequences, demonstrating the approach with various examples and extending to broader polynomial classes.

## Contribution

It introduces a matrix algebra method to analyze Sheffer-Appell polynomials, providing new identities and differential equations not previously established.

## Key findings

- Derived new identities and differential equations for Sheffer-Appell polynomials.
- Presented a matrix approach to obtain generating functions.
- Extended results to a broader class of polynomial sequences.

## 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.