Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1)

Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte

Research output: Contribution to journal › Article

25 Citations (Scopus)

Abstract

A class of classical solutions to the q-Painlevé equation of type (A1 +A1) (1) (a q-difference analog of the Painlevé II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this q-Painlevé equation to the Painlevé II equation and its hypergeometric solutions are discussed. The continuous limit of these hypergeometric solutions to the Airy function is obtained through a uniform asymptotic expansion of their integral representation.

Original languageEnglish
Article number84619
JournalInternational Mathematics Research Notices
Volume2006
DOIs
Publication statusPublished - Dec 5 2006

Fingerprint

Basic Hypergeometric Functions
Uniform Asymptotic Expansion
Airy Functions
Classical Solution
Integral Representation
Analogue
Class
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1). / Hamamoto, Taro; Kajiwara, Kenji; Witte, Nicholas S.

In: International Mathematics Research Notices, Vol. 2006, 84619, 05.12.2006.

Research output: Contribution to journal › Article

Hamamoto, T, Kajiwara, K & Witte, NS 2006, 'Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1)', International Mathematics Research Notices, vol. 2006, 84619. https://doi.org/10.1155/IMRN/2006/84619
Hamamoto T, Kajiwara K, Witte NS. Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1). International Mathematics Research Notices. 2006 Dec 5;2006. 84619. https://doi.org/10.1155/IMRN/2006/84619
Hamamoto, Taro ; Kajiwara, Kenji ; Witte, Nicholas S. / Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1). In: International Mathematics Research Notices. 2006 ; Vol. 2006.
@article{c58542dcbd0c40ad8efa520ebd7fc6cd,
title = "Hypergeometric solutions to the q-Painlev{\'e} equation of type (A 1 +A1́)(1)",
abstract = "A class of classical solutions to the q-Painlev{\'e} equation of type (A1 +A1) (1) (a q-difference analog of the Painlev{\'e} II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this q-Painlev{\'e} equation to the Painlev{\'e} II equation and its hypergeometric solutions are discussed. The continuous limit of these hypergeometric solutions to the Airy function is obtained through a uniform asymptotic expansion of their integral representation.",
author = "Taro Hamamoto and Kenji Kajiwara and Witte, {Nicholas S.}",
year = "2006",
month = "12",
day = "5",
doi = "10.1155/IMRN/2006/84619",
language = "English",
volume = "2006",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",

}

TY - JOUR

T1 - Hypergeometric solutions to the q-Painlevé equation of type (A 1 +A1́)(1)

AU - Hamamoto, Taro

AU - Kajiwara, Kenji

AU - Witte, Nicholas S.

PY - 2006/12/5

Y1 - 2006/12/5

N2 - A class of classical solutions to the q-Painlevé equation of type (A1 +A1) (1) (a q-difference analog of the Painlevé II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this q-Painlevé equation to the Painlevé II equation and its hypergeometric solutions are discussed. The continuous limit of these hypergeometric solutions to the Airy function is obtained through a uniform asymptotic expansion of their integral representation.

AB - A class of classical solutions to the q-Painlevé equation of type (A1 +A1) (1) (a q-difference analog of the Painlevé II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this q-Painlevé equation to the Painlevé II equation and its hypergeometric solutions are discussed. The continuous limit of these hypergeometric solutions to the Airy function is obtained through a uniform asymptotic expansion of their integral representation.

UR - http://www.scopus.com/inward/record.url?scp=33751532980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751532980&partnerID=8YFLogxK

U2 - 10.1155/IMRN/2006/84619

DO - 10.1155/IMRN/2006/84619

M3 - Article

AN - SCOPUS:33751532980

VL - 2006

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

M1 - 84619

ER -

Access to Document