Hypergeometric solutions to the q-Painlevé equation of type ${(A_1+A_1^{'})}^{(1)}$

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.