Recurrence relations for polynomial sequences via Riordan matrices

TL;DR

This paper develops a unified framework using Riordan matrices to derive recurrence relations for generalized Appell polynomial families, connecting classical sequences and generalized umbral calculus.

Contribution

It introduces a novel approach employing Riordan group techniques to unify and extend recurrence relations for various polynomial sequences.

Findings

Derived general recurrence relations for polynomial families

Unified classical and generalized polynomial sequences

Applied Riordan matrices and Hadamard products in polynomial analysis

Abstract

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different families of polynomials. Moreover using the Hadamard product of series we get a general recurrence relation for the polynomial sequences associated to the so called generalized umbral calculus.