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Generating functions related to the Okamoto polynomials for the Painlevé IV equation

Published online by Cambridge University Press:  17 April 2009

Hiromichi Goto  and
Kenji Kajiwara
Hiromichi Goto
Affiliation:
Graduate School of Mathematics, Kyushu University, 6–10–1 Hakozaki, Fukuoka 812–8581, Japan
Kenji Kajiwara
Affiliation:
Graduate School of Mathematics, Kyushu University, 6–10–1 Hakozaki, Fukuoka 812–8581, Japan and School of Mathematics and Statistics F07, The University of Sydney, Sydney 2006, Australia
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We construct generating functions for the entries of Hankel determinant formula for the Okamoto polynomials which characterise a class of rational solutions to the Painlevé IV equation. Generating functions are characterised as asymptotic expansions of log derivative of Ai and Bi, which are solutions of the Airy equation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 517 - 526
Copyright
Copyright © Australian Mathematical Society 2005

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