  In this work, based on quantum operator Hermite polynomials and Weyl's
mapping rule, we find a generation function of the two-variable Hermite
polynomials. And then, noting that the Weyl ordering is invariant under the
similar transformations, we obtain another generalized differential expression
related to the Hermite polynomials. Those identites can be applied to
investigate the nonclasscial properties of quantum optical fields.
