## Nagoya Mathematical Journal

### Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations

#### 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.

#### Article information

Source
Nagoya Math. J., Volume 159 (2000), 179-200.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631457

Mathematical Reviews number (MathSciNet)
MR1783569

Zentralblatt MATH identifier
0972.34077

#### Citation

Fukutani, Satoshi; Okamoto, Kazuo; Umemura, Hiroshi. Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations. Nagoya Math. J. 159 (2000), 179--200. https://projecteuclid.org/euclid.nmj/1114631457

#### References

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