On the Weyl Ordering operation

A Weyl ordering product operation (with its representative symbol) is introduced. On the basis of the operation, a technique of integration within a Weyl ordered product is put forward. Application of the technique to the coherent state representation leads us to derive the Weyl ordered forms of some important operators in quantum mechanics, which can be rigorously checked by the relation between our Weyl ordering product operation and the Weyl correspondence rule.