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Multivariate versions of classical orthogonal polynomials such as Jacobi,Hahn, Laguerre and Meixner are reviewed and their connection explored byadopting a probabilistic approach. Hahn and Meixner polynomials are interpretedas posterior mixtures of Jacobi and Laguerre polynomials, respectively. Byusing known properties of gamma point processes and related transformations, anew infinite-dimensional version of Jacobi polynomials is constructed withrespect to the size-biased version of the Poisson--Dirichlet weight measure andto the law of the gamma point process from which it is derived.

bernoulli

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