Hypergeometric Solutions to the q-Painlevé Equation of Type (A1+A1')(1)
Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte
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.
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