Differential system related to Krawtchouk polynomials: iterated regularisation and Painlev\'e equation
Classical Analysis and ODEs
2026-03-31 v2 Mathematical Physics
math.MP
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 Painlev\'e V equation via iterative regularisation. Furthermore, we explore how iterative regularisation yields polynomial systems and enables us to find decompositions of certain birational transformations.
Cite
@article{arxiv.2411.18192,
title = {Differential system related to Krawtchouk polynomials: iterated regularisation and Painlev\'e equation},
author = {Galina Filipuk and Juan F. Mañas-Mañas and Juan J. Moreno-Balcázar and Cristina Rodríguez-Perales},
journal= {arXiv preprint arXiv:2411.18192},
year = {2026}
}
Comments
This is a preprint of the published version in Numerical Algorithms