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The Rahman Polynomials Are Bispectral
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
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The Rahman Polynomials Are Bispectral
Інший ID:
2000 Mathematics Subject Classification: 33C45; 22E45
Посилання:
The Rahman Polynomials Are Bispectral / F.A. Grünbaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 34 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
467
Завантажень:
181
Анотація:
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.
