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

Hiromichi Goto; Kenji Kajiwara

doi:10.1017/s0004972700038521

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

Hiromichi Goto
, Kenji Kajiwara

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	517-526
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	71
Issue number	3
DOIs	https://doi.org/10.1017/s0004972700038521
Publication status	Published - Jun 2005

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1017/s0004972700038521

Cite this

@article{7f9806c7a5404fe8b7d0246bf5d5f8c7,

title = "Generating functions related to the Okamoto polynomials for the Painlev{\'e} IV equation",

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 Painlev{\'e} 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.",

author = "Hiromichi Goto and Kenji Kajiwara",

year = "2005",

month = jun,

doi = "10.1017/s0004972700038521",

language = "English",

volume = "71",

pages = "517--526",

journal = "Bulletin of the Australian Mathematical Society",

issn = "0004-9727",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

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

AU - Goto, Hiromichi

AU - Kajiwara, Kenji

PY - 2005/6

Y1 - 2005/6

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 - https://www.scopus.com/pages/publications/22944489272

UR - https://www.scopus.com/pages/publications/22944489272#tab=citedBy

U2 - 10.1017/s0004972700038521

DO - 10.1017/s0004972700038521

M3 - Article

AN - SCOPUS:22944489272

SN - 0004-9727

VL - 71

SP - 517

EP - 526

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this