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 |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| 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| _version_ | 1862703296669548544 |
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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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| first_indexed | 2025-12-07T16:48:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147372 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:48:00Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT grunbaumfa therahmanpolynomialsarebispectral AT grunbaumfa rahmanpolynomialsarebispectral |