Abstract
We derive some new generating function formulae of the two-variable Hermite polynomials, such as Hn,2m (x), H2n,2m (x,y), and H2n+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.
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