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A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the “classical” orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.
Mots-clés : cumulative Bernoulli trials; multivariate Markov chains; $9-j$ symbols; transition kernel; Askey–Wilson polynomials; eigenvalue problem; trinomial distribution; Krawtchouk polynomials. 
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Michael R. Hoare; Mizan Rahman. A Probablistic Origin for a New Class of Bivariate Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a88/

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