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A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation

Clarkson, Peter, Law, Chun-Kong, Lin, Chia-Hua (2023) A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation. Symmetry, Integrability and Geometry: Methods and Applications, 19 . Article Number 080. ISSN 1815-0659. (doi:10.3842/SIGMA.2023.080) (KAR id:103469)

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Abstract

We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlevé equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation which determines the Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.

Item Type: Article
DOI/Identification number: 10.3842/SIGMA.2023.080
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: University of Kent (https://ror.org/00xkeyj56)
Depositing User: Peter Clarkson
Date Deposited: 27 Oct 2023 10:06 UTC
Last Modified: 09 Jan 2024 20:23 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/103469 (The current URI for this page, for reference purposes)

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