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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 11 scientific papers (total in 11 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 (11)
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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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\paper The Rahman Polynomials Are Bispectral
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    • This publication is cited in the following 11 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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