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arXiv · 2411.18192

Differential system related to Krawtchouk polynomials: iterated regularisation and Painlev\'e equation

Galina Filipuk·Juan F. Mañas-Mañas·Juan J. Moreno-Balcázar·Cristina Rodríguez-Perales
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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.

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Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar, Cristina Rodríguez-Perales. 2024-11-27. Differential system related to Krawtchouk polynomials: iterated regularisation and Painlev\'e equation. https://doi.org/10.1007/s11075-025-02299-z

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