Connection preserving deformations and $q$-semi-classical orthogonal polynomials
Exactly Solvable and Integrable Systems
2010-05-10 v2
Abstract
We present a framework for the study of -difference equations satisfied by -semi-classical orthogonal systems. As an example, we identify the -difference equation satisfied by a deformed version of the little -Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for -. We obtain a parameterization of the associated linear problem in terms of orthogonal polynomial variables and find the relation between this parameterization and that of Jimbo and Sakai.
Keywords
Cite
@article{arxiv.0906.0640,
title = {Connection preserving deformations and $q$-semi-classical orthogonal polynomials},
author = {Christopher M. Ormerod and Nicholas S. Witte and Peter J. Forrester},
journal= {arXiv preprint arXiv:0906.0640},
year = {2010}
}
Comments
32 Pages, extended the study of the recursion relations, more references