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

Clarkson, Peter and Law, Chun-Kong and Lin, Chia-Hua (2016) A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation. [Preprint] (doi:10.48550/arXiv.1609.00495) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:59907)

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Official URL:
https://doi.org/10.48550/arXiv.1609.00495

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: Preprint
DOI/Identification number: 10.48550/arXiv.1609.00495
Refereed: No
Other identifier: https://arxiv.org/abs/1609.00495
Name of pre-print platform: arXiv
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
Depositing User: Peter Clarkson
Date Deposited: 18 Jan 2017 06:21 UTC
Last Modified: 27 Oct 2023 07:37 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/59907 (The current URI for this page, for reference purposes)

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