### 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 |
---|---|

Article number | 84619 |

Journal | International Mathematics Research Notices |

Volume | 2006 |

DOIs | |

Publication status | Published - Dec 5 2006 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*International Mathematics Research Notices*,

*2006*, [84619]. https://doi.org/10.1155/IMRN/2006/84619

**Hypergeometric solutions to the q-Painlevé equation of type (A _{1} +A_{1}́)^{(1)}.** / Hamamoto, Taro; Kajiwara, Kenji; Witte, Nicholas S.

Research output: Contribution to journal › Article

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*International Mathematics Research Notices*, vol. 2006, 84619. https://doi.org/10.1155/IMRN/2006/84619

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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 -