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

New identities about operator Hermite polynomials and their related integration formulas