The properties of Weyl ordered products of operators are investigated and the technique of integration within Weyl ordered product (IWWP) is introduced. The overcompleteness relation of the coherent state is then recast into Weyl ordered form. In so doing, a new approach for Weyl ordering quantum mechanical operators is presented.
We investigate the properties of the Weyl-ordered polynomials Tm,n by the technique of integration within a Weyl-ordered product (IWWOP) and the Weyl quantization rule. The introduction of the Weyl-ordering symbol ⋮⋮ and the IWWOP provide us with a convenient approach for deriving the Weyl-ordered form of the product of Tm,n and other operators. The Weyl-ordered Dirac's δ-function form of the Wigner operator can also directly lead us to the Weyl quantization formalism for the functions of radial vaiables.