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

Hiromichi Goto, Kenji Kajiwara

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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. Copyright Clearance Centre, Inc.

Original languageEnglish
Pages (from-to)517-526
Number of pages10
JournalBulletin of the Australian Mathematical Society
Volume71
Issue number3
Publication statusPublished - Jun 1 2005

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Generating Function
Hankel Determinant
Rational Solutions
Polynomial
Clearance
Asymptotic Expansion
Derivative
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Generating functions related to the Okamoto polynomials for the Painlevé IV equation. / Goto, Hiromichi; Kajiwara, Kenji.

In: Bulletin of the Australian Mathematical Society, Vol. 71, No. 3, 01.06.2005, p. 517-526.

Research output: Contribution to journalArticle

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