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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 065, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.065 (Mi sigma191) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The Rahman Polynomials Are Bispectral

F. Alberto Grünbaum

Department of Mathematics, University of California, Berkeley, CA 94720, USA
Full-text PDF (208 kB) Citations (9)
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DOI: https://doi.org/10.3842/SIGMA.2007.065
Abstract: 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.
Keywords: bispectral property; multivariable polynomials; rings of commuting difference operators.
Received: February 1, 2007; in final form April 22, 2007; Published online May 3, 2007
Bibliographic databases:
Document Type: Article
MSC: 33C45; 22E45
Language: English
Citation: F. Alberto Grünbaum, “The Rahman Polynomials Are Bispectral”, SIGMA, 3 (2007), 065, 11 pp.
Citation in format AMSBIB
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\by F.~Alberto Gr\"unbaum
\paper The Rahman Polynomials Are Bispectral
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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