Lies Boelen, Galina Filipuk, Christophe Smet, Walter Van Assche, Lun Zhang
Published 2012-04-23, updated 2012-11-30Version 2
We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painlev\'e equation when viewed as functions of one of the parameters in the weight.
Comments: 15 pages, 4 figures, references added with more details and explanations, to appear in Journal of Difference Equations and Applications
Orthogonal polynomials on a bi-lattice
Recurrence Coefficients of a New Generalization of the Meixner Polynomials
Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlevé equations
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