The generalized Krawtchouk polynomials and the fifth Painlevé equation

Details The generalized Krawtchouk polynomials and the fifth Painlevé equation The generalized Krawtchouk polynomials and the fifth Painlevé equation

2012-04-23

arxiv.org/abs/1204.5070v1

Mathematics

Classical Analysis and ODEs

11 pages, 3 figures

Scientific paper

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.

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