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

Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte

Research output: Contribution to journalArticle

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

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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 journalArticle

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