Abstract: Wigner operator and Weyl prescription are studied by virtue of the skill of differential-integral and the method of operators＇ differential quotient. The differential formula of Wigner operator in normal ordering is given, and new differential formulae of some special functions are obtained. It is more important that the integral divergent difficulty is smoothed away and the differential formula of Wigner operator and the Weyl prescription in anti-normal ordering are derived. Several examples are calculated.

Key words: ordered operator, Wigner operator, differential quotient of operators, integral divergence