arXiv subjects
Publications and source records attributed to Taro Hamamoto.
We consider the q-Painlevé equation of type $A_4^{(1)}$ (a version of q-Painlevé V equation) and construct a family of solutions expressible in terms of certain basic hypergeometric series. We also present the determinant formula for the solutions.
A class of classical solutions to the $q$-Painlevé equation of type $(A_1+A_1')^{(1)}$ (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.