### 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 language | English |
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Pages (from-to) | 517-526 |

Number of pages | 10 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 71 |

Issue number | 3 |

Publication status | Published - Jun 1 2005 |

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### 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.

Research output: Contribution to journal › Article

*Bulletin of the Australian Mathematical Society*, vol. 71, no. 3, pp. 517-526.

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TY - JOUR

T1 - Generating functions related to the Okamoto polynomials for the Painlevé IV equation

AU - Goto, Hiromichi

AU - Kajiwara, Kenji

PY - 2005/6/1

Y1 - 2005/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=22944489272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22944489272&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22944489272

VL - 71

SP - 517

EP - 526

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 3

ER -