# $q$-Discrete Painlevé equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials - Mathematics > Classical Analysis and ODEs

$q$-Discrete Painlevé equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials - Mathematics > Classical Analysis and ODEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: We present an asymmetric $q$-Painlev\-e equation. We will derive this using$q$-orthogonal polynomials with respect to generalized Freud weights: theirrecurrence coefficients will obey this $q$-Painlev\-e equation up to a simpletransformation. We will show a stable method of computing a special solutionwhich gives the recurrence coefficients. We establish a connection with$\alpha-q-P V$.

Author: Lies Boelen, Christophe Smet, Walter Van Assche

Source: https://arxiv.org/