A Probablistic Origin for a New Class of Bivariate Polynomials

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 corresp...

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Дата:2008
Автори: Hoare, M.R., Rahman, M.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2008
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/148000
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1480002019-02-17T01:26:56Z A Probablistic Origin for a New Class of Bivariate Polynomials Hoare, M.R. Rahman, M. 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. 2008 Article A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C45; 60J05 http://dspace.nbuv.gov.ua/handle/123456789/148000 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Hoare, M.R.
Rahman, M.
spellingShingle Hoare, M.R.
Rahman, M.
A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Hoare, M.R.
Rahman, M.
author_sort Hoare, M.R.
title A Probablistic Origin for a New Class of Bivariate Polynomials
title_short A Probablistic Origin for a New Class of Bivariate Polynomials
title_full A Probablistic Origin for a New Class of Bivariate Polynomials
title_fullStr A Probablistic Origin for a New Class of Bivariate Polynomials
title_full_unstemmed A Probablistic Origin for a New Class of Bivariate Polynomials
title_sort probablistic origin for a new class of bivariate polynomials
publisher Інститут математики НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/148000
citation_txt A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
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