An algebraic proof for the Umemura polynomials for the third Painlevé equation

Clarkson, Peter and Law, Chun-Kong and Lin, Chia-Hua (2016) An algebraic proof for the Umemura polynomials for the third Painlevé equation. Technical report. arxiv.org (Full text available)

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https://arxiv.org/abs/1609.00495

Abstract

We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials.

Item Type: Monograph (Technical report)
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter A Clarkson
Date Deposited: 18 Jan 2017 06:21 UTC
Last Modified: 07 Aug 2018 09:24 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/59907 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
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