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26 April 2024

» arxiv » 0809.1431

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Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials
Robert C. Griffiths ; Dario Spanò ;
Date:	9 Sep 2008
Abstract:	Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre, Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior mixtures of Jacobi and Laguerre polynomials, respectively. By using known properties of Gamma point processes and related transformations, an infinite-dimensional version of Jacobi polynomials is constructed with respect to the size-biased version of the Poisson-Dirichlet weight measure and to the law of the Gamma point process from which it is derived.
Source:	arXiv, 0809.1431
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