A linear algebra approach to hybrid polynomial sequences

TL;DR

This paper introduces a linear algebra method to analyze hybrid Sheffer polynomial sequences, deriving their recurrence relations and differential equations using Pascal and Wronskian matrices, and extends results to mixed Sheffer polynomials.

Contribution

It presents a novel linear algebra framework for studying hybrid Sheffer polynomials, including derivation of key properties and extension to mixed types.

Findings

Derived recurrence relations for hybrid Sheffer polynomials

Established differential equations using Pascal and Wronskian matrices

Extended results to mixed Sheffer polynomial types

Abstract

In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and relationships between the Pascal functional matrices and the Wronskian matrices. The corresponding results for some mixed type Sheffer polynomials are also obtained.