(p,q)-Rogers-Szego polynomial and the (p,q)-oscillator

TL;DR

This paper introduces a (p,q)-analogue of the Rogers-Szego polynomial, linking it to the (p,q)-oscillator algebra, thus extending classical q-analogs to a broader (p,q) framework.

Contribution

It defines a new (p,q)-Rogers-Szego polynomial and establishes its connection with the (p,q)-oscillator algebra, generalizing existing q-analogues.

Findings

The (p,q)-Rogers-Szego polynomial is explicitly constructed.

The polynomial is shown to be associated with the (p,q)-oscillator algebra.

This generalization extends classical q-analogues to the (p,q) setting.

Abstract

A (p,q)-analogue of the classical Rogers-Szego polynomial is defined by replacing the q-binomial coefficient in it by the (p,q)-binomial coefficient. Exactly like the Rogers-Szego polynomial is associated with the q-oscillator algebra it is found that the (p,q)-Rogers-Szego polynomial is associated with the (p,q)-oscillator algebra.