The Rahman Polynomials Are Bispectral
Classical Analysis and ODEs
2008-04-24 v1 Mathematical Physics
math.MP
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
Cite
@article{arxiv.0705.0468,
title = {The Rahman Polynomials Are Bispectral},
author = {F. Alberto Grünbaum},
journal= {arXiv preprint arXiv:0705.0468},
year = {2008}
}