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Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations

Published online by Cambridge University Press:  22 January 2016

Satoshi Fukutani ,
Kazuo Okamoto  and
Hiroshi Umemura
Satoshi Fukutani
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
Kazuo Okamoto
Affiliation:
Graduate School of Mathematical Science, University of Tokyo, Maguro-ku, Tokyo 153-8914, Japan
Hiroshi Umemura
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan, umemura@math.nagoya-u.ac.jp
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Abstract

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

Keywords

34M5533E17
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 159 , 2000 , pp. 179 - 200
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

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