Combinatorial And Analytic Properties Of The N-Dimensional Hermite Polynomials

Keywords

Generating functions; Kibble–Slepian formula; Multiset enumeration; n-Dimensional Hermite polynomials; Weighted matchings

Abstract

We investigate some combinatorial and analytic properties of the n-dimensional Hermite polynomials introduced by Hermite in the late 19-th century. We derive combinatorial interpretations and recurrence relations for these polynomials. We also establish a new linear generating function and a Kibble–Slepian formula for the n-dimensional Hermite polynomials which generalize the Kibble–Slepian formula for the univariate Hermite polynomials and the Poisson kernel (Mehler formula) for the n-dimensional Hermite polynomials.

Publication Date

5-1-2017

Publication Title

Journal of Mathematical Analysis and Applications

Volume

449

Issue

1

Number of Pages

368-381

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2016.11.073

Socpus ID

85008423118 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85008423118

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