Combinatorial and analytic properties of the n-dimensional Hermite polynomials

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• 作者：Mourad E.H. Ismail^a ; ^{mourad.eh.ismail@gmail.com} ; Plamen Simeonov^b ; ^{simeonovp@uhd.edu}
• 关键词：n-Dimensional Hermite polynomials ; Generating functions ; Multiset enumeration ; Weighted matchings ; Kibble&ndash ; Slepian formula
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：368-381
• 全文大小：413 K
• 卷排序：449

文摘

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.