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Clarkson, Peter; Law, Chun-Kong; Lin, Chia-Hua (2016)
Publisher: arxiv.org
Languages: English
Types: Book
Subjects: QA351, QA372

Classified by OpenAIRE into

arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems
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.

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