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Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials

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Griffiths, Robert C. and Spanò, Dario. (2011) Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials. Bernoulli , Vol.17 (No.3). pp. 1095-1125.

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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, a new 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Orthogonal polynomials
Journal or Publication Title:	Bernoulli
Publisher:	International Statistical Institute
Date:	2011
Volume:	Vol.17
Number:	No.3
Page Range:	pp. 1095-1125
Identification Number:	10.3150/10-BEJ305
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35496