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

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

2008-08-07

arxiv.org/abs/0808.0982v1

Mathematics

Classical Analysis and ODEs

16 pages, 4 figures. Accepted, to appear in Journal of Difference Equations and Applications

Scientific paper

We present an asymmetric $q$-Painlev\'e equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlev\'e 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 $\alpha-q-P_V$.

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