Abstract
It is known that for a normalN(0, 1) random variable (r.v.) Y0 the expectation of the Hermite polynomial Hn in Y0 is equal to zero, i.e.,E[Hn(Y0)]=0, n≥1. We give examples of other distributions satisfying this condition as well as some characterizations of these distributions. We show that for some subsets of Hermite polynomials the orthogonality measure is not unique.
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