Some operator identities related to $q-$Hermite polynomials

TL;DR

This paper explores $q$-analogues of normal ordering for the operator $(X+sD)^n$, providing new identities that extend classical operator relations into the $q$-deformed setting.

Contribution

It introduces novel $q$-operator identities related to $q$-Hermite polynomials, expanding the understanding of $q$-analogues in operator theory.

Findings

Derived $q$-analogues of normal ordering for $(X+sD)^n$

Established new identities involving $q$-Hermite polynomials

Extended classical operator identities into the $q$-deformed framework

Abstract

Some $q-$analogues of the normal ordering of the operator $(X+sD)^n$ on the polynomials are derived.