The Rahman Polynomials Are Bispectral

F. Alberto Grünbaum

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

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.

Détail

Keywords: bispectral property; multivariable polynomials; rings of commuting difference operators.

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