The generalized Krawtchouk polynomials and the fifth Painlevé equation

2012/04/23 by Lies Boelen, Galina Filipuk, Boelen, Lies +7
Chemistry · Mathematics · Physics and Astronomy · #33C47 #33E17 #34M55 #42C05 #65Q30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1204.5070

openalex publication_date 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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