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arXiv · 0906.0640

Connection preserving deformations and $q$-semi-classical orthogonal polynomials

Christopher M. Ormerod·Nicholas S. Witte·Peter J. Forrester
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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 $q$-$\mathrm{P}_{\mathrm{VI}}$. 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.

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Christopher M. Ormerod, Nicholas S. Witte, Peter J. Forrester. 2010-05-07. Connection preserving deformations and $q$-semi-classical orthogonal polynomials. https://arxiv.org/abs/0906.0640

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