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 |
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Автори: | , |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2008
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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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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 |
work_keys_str_mv |
AT hoaremr aprobablisticoriginforanewclassofbivariatepolynomials AT rahmanm aprobablisticoriginforanewclassofbivariatepolynomials AT hoaremr probablisticoriginforanewclassofbivariatepolynomials AT rahmanm probablisticoriginforanewclassofbivariatepolynomials |
first_indexed |
2023-05-20T17:29:00Z |
last_indexed |
2023-05-20T17:29:00Z |
_version_ |
1796153396870250496 |