Hermite polynomials. (English) Zbl 0961.33008

Fisk, Steve

J. Comb. Theory, Ser. A 91, No. 1-2, 334-336 (2000).

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).

Reviewer: H.-J.Glaeske (Jena)

MSC:

33C45

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

Keywords:

zeros; Hermite polynomial