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Deformed Complex Hermite Polynomials (1410.3908v3)
Published 15 Oct 2014 in math-ph and math.MP
Abstract: We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along the way we also work out some additional properties of the (undeformed) complex Hermite polynomials and their relationships to the standard Hermite polynomials (of a single real variable).