The generalized Krawtchouk polynomials and the fifth Painlevé equation

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 Painlevé equation when viewed as functions of one of the parameters...

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Bibliographic Details
Published in:arXiv.org 2012-11
Main Authors: Boelen, Lies, Filipuk, Galina, Smet, Christophe, Walter Van Assche, Zhang, Lun
Format: Article
Language:English
Subjects:
Discrete systems
Mathematical analysis
Polynomials
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Summary: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 Painlevé equation when viewed as functions of one of the parameters in the weight.
ISSN:2331-8422