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arXiv · 0812.3879

A Probablistic Origin for a New Class of Bivariate Polynomials

Michael R. Hoare·Mizan Rahman
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Abstract

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.

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Michael R. Hoare, Mizan Rahman. 2008-12-19. A Probablistic Origin for a New Class of Bivariate Polynomials. https://doi.org/10.3842/sigma.2008.089

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