New identities about operator Hermite polynomials and their related integration formulas

By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation, we derive some new identities about operator Hermite polynomials in both the single-and two-variable cases. We also find a binomial-like theorem between the single-variable Hermite polynomials and the two-variable Hermite polynomials. Application of these identities in deriving new integration formulas, but without really doing the integration in the usual sense, is demonstrated.