Multi-indexed Wilson and Askey-Wilson Polynomials
Mathematical Physics
2017-05-24 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of 'virtual state solutions' of type I and II, in a similar way to the multi-indexed Laguerre, Jacobi and (q-)Racah polynomials reported earlier.
Keywords
Cite
@article{arxiv.1207.5584,
title = {Multi-indexed Wilson and Askey-Wilson Polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1207.5584},
year = {2017}
}
Comments
30 pages. Three references added. To appear in J.Phys.A. arXiv admin note: text overlap with arXiv:1203.5868