On Simple Characterisations of Sheffer psi- polynomials and Related Propositions of the Calculus of Sequences

TL;DR

This paper explores simple characterizations of Sheffer psi-polynomials within the framework of psi-calculus, an extension of finite operator calculus originating in 1936, highlighting its automatic extension properties.

Contribution

It provides new characterizations of Sheffer psi-polynomials and discusses their relation to the broader psi-calculus framework, extending classical finite operator calculus.

Findings

Characterizations of Sheffer psi-polynomials derived

Connections established between psi-calculus and classical calculus

Extensions of finite operator calculus discussed

Abstract

A calculus of sequences started in 1936 opened the way for future extensions of umbral calculus in its finite operator form. Because of historically established notation we call it the psi-calculus.It appears in parts to be almost automatic extension of the standard classical finite operator calculus.