## Entropy of Hermite polynomials with application to the harmonic oscillator.(English)Zbl 0866.33006

In this interesting paper the author investigates the entropy of Hermite polynomials and more general orthogonal polynomials for the Freud weight $$w(x)= \exp (-|x |^m)$$ on $$R$$. Moreover it is shown how these entropies are related to the information entropy of the one-dimensional harmonic oscillator.

### MSC:

 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

### Keywords:

Hermite polynomials; Freud weight; harmonic oscillator
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