2-iterated Sheffer polynomials

TL;DR

This paper introduces 2-iterated Sheffer polynomials, exploring their generating functions, operational representations, and properties using Riordan arrays, and provides new examples within this polynomial family.

Contribution

It presents the first detailed study of 2-iterated Sheffer polynomials, including their definitions, properties, and connections to Riordan arrays.

Findings

Derived generating functions and determinantal definitions.

Established properties such as quasi-monomiality.

Presented new examples of 2-iterated Sheffer polynomials.

Abstract

In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a determinantal definition for these polynomials is established. The quasi-monomial and other properties of these polynomials are derived. The generating function, determinantal definition, quasi-monomial and other properties for some new members belonging to this family are also considered.