# 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

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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) Q Science > QA Mathematics (inc Computing science) > QA351 Special functionsQ Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Peter A Clarkson 18 Jan 2017 06:21 UTC 29 May 2019 18:33 UTC https://kar.kent.ac.uk/id/eprint/59907 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-8777-5284