Q-difference polynomial

A Q-difference polynomial is an extension of the classical notion of polynomials in the context of difference equations and q-calculus. It is primarily used in the field of quantum calculus, where the concept of q-analogues is prevalent. In a basic sense, a Q-difference polynomial can be viewed as a polynomial where the variable \( x \) is replaced by \( q^x \), where \( q \) is a fixed non-zero complex number (often assumed to be non-negative).