ABSTRACT. We prove that the complex Hermite polynomials H m,n on the complex plane C can be realized as the Fourier-Wigner transform V of the well-known real Hermite functions h n on real line R. This reduces considerably the Wong's proof [19, Chapter 21] giving the explicit expression of V(h m , h n ) in terms of the Laguerre polynomials. Moreover, we derive a new generating function for the H m,n as well as some new integral identities.
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