The Rahman Polynomials Are Bispectral

In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to M. Hoare and M. Rahman. I indicate here that these polynomials are bispectral. This should be just one of the many rema...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2007
1. Verfasser: Grünbaum, F.A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2007
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147372
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The Rahman Polynomials Are Bispectral / F.A. Grünbaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 34 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Grünbaum, F.A.
author_facet Grünbaum, F.A.
citation_txt The Rahman Polynomials Are Bispectral / F.A. Grünbaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 34 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to M. Hoare and M. Rahman. I indicate here that these polynomials are bispectral. This should be just one of the many remarkable properties enjoyed by these polynomials. For several challenges, including finding a general proof of some of the facts displayed here the reader should look at the last section of this paper.
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spelling Grünbaum, F.A.
2019-02-14T14:48:36Z
2019-02-14T14:48:36Z
2007
The Rahman Polynomials Are Bispectral / F.A. Grünbaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 34 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 33C45; 22E45
https://nasplib.isofts.kiev.ua/handle/123456789/147372
In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to M. Hoare and M. Rahman. I indicate here that these polynomials are bispectral. This should be just one of the many remarkable properties enjoyed by these polynomials. For several challenges, including finding a general proof of some of the facts displayed here the reader should look at the last section of this paper.
This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. I am very thankful to a couple of referees who read the paper with great care and pointed out typos as well as ways to improve the presentation. The author was supported in part by NSF Grant # 0603901.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Rahman Polynomials Are Bispectral
Article
published earlier
spellingShingle The Rahman Polynomials Are Bispectral
Grünbaum, F.A.
title The Rahman Polynomials Are Bispectral
title_full The Rahman Polynomials Are Bispectral
title_fullStr The Rahman Polynomials Are Bispectral
title_full_unstemmed The Rahman Polynomials Are Bispectral
title_short The Rahman Polynomials Are Bispectral
title_sort rahman polynomials are bispectral
url https://nasplib.isofts.kiev.ua/handle/123456789/147372
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