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arXiv · 1204.5070

The generalized Krawtchouk polynomials and the fifth Painlevé equation

Lies Boelen·Galina Filipuk·Christophe Smet·Walter Van Assche·Lun Zhang
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Abstract

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.

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Lies Boelen, Galina Filipuk, Christophe Smet, Walter Van Assche, Lun Zhang. 2012-11-30. The generalized Krawtchouk polynomials and the fifth Painlevé equation. https://arxiv.org/abs/1204.5070

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