The generalized Krawtchouk polynomials and the fifth Painlev\'e equation
Classical Analysis and ODEs
2012-12-03 v2
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 Painlev\'e equation when viewed as functions of one of the parameters in the weight.
Cite
@article{arxiv.1204.5070,
title = {The generalized Krawtchouk polynomials and the fifth Painlev\'e equation},
author = {Lies Boelen and Galina Filipuk and Christophe Smet and Walter Van Assche and Lun Zhang},
journal= {arXiv preprint arXiv:1204.5070},
year = {2012}
}
Comments
15 pages, 4 figures, references added with more details and explanations, to appear in Journal of Difference Equations and Applications