## 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 language | English |
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Article number | 84619 |

Journal | International Mathematics Research Notices |

Volume | 2006 |

DOIs | |

Publication status | Published - 2006 |

## All Science Journal Classification (ASJC) codes

- General Mathematics

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