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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-05-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/065/ |
| _version_ | 1818127525911461888 |
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| author | F. Alberto Grünbaum |
| author_facet | F. Alberto Grünbaum |
| author_sort | F. Alberto Grünbaum |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-11T07:18:45Z |
| format | Article |
| id | doaj.art-437580b8de074dafa25d04fe41c3ca46 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-11T07:18:45Z |
| publishDate | 2007-05-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-437580b8de074dafa25d04fe41c3ca462022-12-22T01:16:08ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-05-013065The Rahman Polynomials Are BispectralF. Alberto GrünbaumIn 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.http://www.emis.de/journals/SIGMA/2007/065/bispectral propertymultivariable polynomialsrings of commuting difference operators |
| spellingShingle | F. Alberto Grünbaum The Rahman Polynomials Are Bispectral Symmetry, Integrability and Geometry: Methods and Applications bispectral property multivariable polynomials rings of commuting difference operators |
| 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 |
| topic | bispectral property multivariable polynomials rings of commuting difference operators |
| url | http://www.emis.de/journals/SIGMA/2007/065/ |
| work_keys_str_mv | AT falbertogrunbaum therahmanpolynomialsarebispectral AT falbertogrunbaum rahmanpolynomialsarebispectral |