Post-quantum complex Itô–Hermite polynomials

We consider the post-quantum analog of the q-2D Itô–Hermite polynomials recently introduced by Ismail and Zhang. Their basic properties are described, such as the zeros set, the Rodrigues formula, the corresponding raising and lowering operators, operational formulas, and the (p, q)-eigenvalue problem they obey. Moreover, we establish some partial generating functions, partial Mehler’s formulas, and integral representations.