Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
Abstract
In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we present a proof for the Laguerre and Jacobi cases. Their bispectral properties are also discussed, which give a method to obtain the coefficients of the recurrence relations explicitly. This paper extends to the Laguerre and Jacobi cases the bispectral techniques recently introduced by G\'omez-Ullate et al. to derive explicit expressions for the coefficients of the recurrence relations satisfied by exceptional polynomials of Hermite type.
Keywords
Cite
@article{arxiv.1509.08213,
title = {Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III},
author = {Satoru Odake},
journal= {arXiv preprint arXiv:1509.08213},
year = {2016}
}
Comments
37 pages. Comments added, typo in (A.15) corrected, reference information updated. To appear in J.Math.Phys