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.
All Science Journal Classification (ASJC) codes
- 数学 (全般)