Multi-indexed (q-)Racah Polynomials
Abstract
As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of `virtual state' vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the `solutions' of the matrix Schr\"odinger equation with negative `eigenvalues', except for one of the two boundary points.
Keywords
Cite
@article{arxiv.1203.5868,
title = {Multi-indexed (q-)Racah Polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1203.5868},
year = {2015}
}
Comments
29 pages. The type II (q-)Racah polynomials are deleted because they can be obtained from the type I polynomials. To appear in J.Phys.A