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arXiv · 0808.0982

$q$-Discrete Painlevé equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials

Lies Boelen·Christophe Smet·Walter Van Assche
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Abstract

We present an asymmetric $q$-Painlevé equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlevé equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection with $α-q-P_V$.

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Lies Boelen, Christophe Smet, Walter Van Assche. 2008-08-07. $q$-Discrete Painlevé equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials. https://arxiv.org/abs/0808.0982

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