Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation

2024/11/27 by Filipuk, Galina, Mañas-Mañas, Juan F., Moreno-Balcázar, Juan J. +1
#34M55 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2411.18192

Abstract

We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities involving the recurrence coefficients of these polynomials and Painlevé V equation via iterative regularisation. Furthermore, we explore how iterative regularisation yields polynomial systems and enables us to find decompositions of certain birational transformations.

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