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

Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte

研究成果: Contribution to journalArticle査読

26 被引用数 (Scopus)

抄録

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.

本文言語英語
論文番号84619
ジャーナルInternational Mathematics Research Notices
2006
DOI
出版ステータス出版済み - 2006

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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