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Hermite Polynomials

✍ Scribed by Steve Fisk

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 59 KB
Volume: 91
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3099

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to the memory of gian-carlo rota

We give an elementary proof that a transformation based on the Hermite polynomials preserves the property of having all real roots.

2000 Academic Press

Consider the following example:

The goal of this paper is to show that the fact that H( f ) has all real roots is not an accident. The H i (x) are the Hermite polynomials. There are many ways of constructing the Hermite polynomials. They are the solutions to the differential equation 0= y"&2xy$+2ny

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