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

Numerical Algorithms 2026 Open access

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Authors: Galina Filipuk, Juan F. Mañas–Mañas, Juan J. Moreno–Balcázar, Cristina Rodríguez–Perales
DOI: 10.1007/s11075-025-02299-z
Cited by: 0
References: 22

Abstract

In this paper we tackle the generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities involving the recurrence coefficients of these polynomials and the fifth Painlevé equation via iterated regularisation. This connection follows an algorithmic procedure avoiding the use of less standardised methods. We further explore how to obtain polynomial systems via iterated regularisation and find decomposition of certain birational transformations into the product of simple ones.

Fields of Study & Subjects

Quantum chaos and dynamical systems Spectral Theory in Mathematical Physics Numerical methods in inverse problems

Publication details

Journal / source
Numerical Algorithms
Publisher
Springer Science and Business Media LLC
Volume
102
Issue
3
Pages
1891–1922
Publication date
2 March 2026
Language
EN