The Rahman Polynomials Are Bispectral

Details The Rahman Polynomials Are Bispectral The Rahman Polynomials Are Bispectral

2007-05-03

arxiv.org/abs/0705.0468v1

SIGMA 3 (2007), 065, 11 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.065

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.

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