Connection preserving deformations and q-semi-classical orthogonal polynomials

2009/06/03 by Ormerod, Christopher M., Witte, Nicholas S., Forrester, Peter J.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.0906.0640

Abstract

We present a framework for the study of q-difference equations satisfied by q-semi-classical orthogonal systems. As an example, we identify the q-difference equation satisfied by a deformed version of the little q-Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for q-P_VI. 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.

Related

• Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions
• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• Jacobi operator, q-difference equation and orthogonal polynomials
• Orthogonality of a new family of q-Sobolev type polynomials
• Non linear difference equations arising from a deformation of the q-Laguerre weight