Hermite polynomials.(English)Zbl 0961.33008

In this paper it is proved, that a so-called Hermite transform which transforms $$x^n$$, $$n\in\mathbb{N}_0$$ into the $$n$$-th Hermite polynomial $$H_n(x)$$ preserves the property of a polynomial having only real roots. (In the proof there is referred to a next paragraph, but it does not exist).

MSC:

 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

zeros; Hermite polynomial
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