Casoratian Identities for the Wilson and Askey-Wilson Polynomials
Mathematical Physics
2015-04-01 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors. These identities form the basis of the equivalence between eigenstate adding and deleting Darboux transformations for solvable (discrete) quantum mechanical systems. Similar identities hold for various reduced form polynomials of the Wilson and Askey-Wilson polynomials, e.g. the continuous q-Jacobi, continuous (dual) (q-)Hahn, Meixner-Pollaczek, Al-Salam-Chihara, continuous (big) q-Hermite, etc.
Keywords
Cite
@article{arxiv.1308.4240,
title = {Casoratian Identities for the Wilson and Askey-Wilson Polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1308.4240},
year = {2015}
}
Comments
31 pages, 2 figures. Comments and references added. To appear in Journal of Approximation Theory