mathfrak{Q}-, mathfrak{P}-, and Weyl-ordering of Squeezing Operators: New Operator Identities and Applications

The basic operator ordering regarding to coordinate-momentum operator is discussed by virtue of the technique of integration within $mathfrak{Q}$ -ordering (all Q are on the left of all P) and $mathfrak{P}$ -ordering (all P are on the left of all Q). We derive new operator-ordering identities about $mathfrak{Q}$ -ordering , $mathfrak{P}$ -ordering and Weyl-ordering of both single-mode and two-mode squeezing operators. Its application in combinatorics is pointed out.