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2000 Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations
Satoshi Fukutani, Kazuo Okamoto, Hiroshi Umemura
Nagoya Math. J. 159: 179-200 (2000).

Abstract

We give a purely algebraic proof that the rational functions $P_n(t),\, Q_n(t)$ inductively defined by the recurrence relation (1), (2) respectively, are polynomials. The proof reveals the Hirota bilinear relations satisfied by the $\tau$-functions.

Citation

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Satoshi Fukutani. Kazuo Okamoto. Hiroshi Umemura. "Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations." Nagoya Math. J. 159 179 - 200, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0972.34077
MathSciNet: MR1783569

Subjects:
Primary: 34M55
Secondary: 33E17, 37K10

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

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Vol.159 • 2000
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