• Corpus ID: 237513877

Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlev\'e equations via the geometric approach

@inproceedings{Dzhamay2021DifferentialEF,
title={Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlev\'e equations via the geometric approach},
author={Anton Dzhamay and Galina Filipuk and Alexander Stokes},
year={2021}
}
• Published 14 September 2021
• Mathematics, Physics
Abstract In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlevé equations using the geometric framework of the Okamoto Space of Initial Conditions. We demonstrate this procedure in two examples. For semi-classical Laguerre polynomials appearing in [HC17], we show how the recurrence coefficients are connected to the fourth Painlevé equation. For discrete orthogonal polynomials…
1 Citations

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