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}
}
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 Okamoto’s space of initial values. 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 associated with… Expand
1 Citations
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