Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

Abstract

We derive some new generating function formulae of the two-variable Hermite polynomials, such asn!m! H 2n+l,2m+k (x, y). We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.