Equivalences of the Multi-Indexed Orthogonal Polynomials
Abstract
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.
Keywords
Cite
@article{arxiv.1309.2346,
title = {Equivalences of the Multi-Indexed Orthogonal Polynomials},
author = {Satoru Odake},
journal= {arXiv preprint arXiv:1309.2346},
year = {2015}
}
Comments
25 pages. Some comments and a reference added. To appear in J.Math.Phys