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This article is cited in 29 scientific papers (total in 29 papers)
A Probablistic Origin for a New Class of Bivariate Polynomials
Michael R. Hoare, Mizan Rahmana a School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
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.
Keywords:
cumulative Bernoulli trials; multivariate Markov chains; $9-j$ symbols; transition kernel; Askey–Wilson polynomials; eigenvalue problem; trinomial distribution; Krawtchouk polynomials.
Received: September 15, 2008; in final form December 15, 2008; Published online December 19, 2008
Citation:
Michael R. Hoare, Mizan Rahman, “A Probablistic Origin for a New Class of Bivariate Polynomials”, SIGMA, 4 (2008), 089, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma342 https://www.mathnet.ru/eng/sigma/v4/p89
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Abstract page: | 647 | Full-text PDF : | 45 | References: | 38 |
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