Hypergeometric Solutions to the q-Painlev\'e Equation of Type   $(A_1+A_1')^{(1)}$
  A class of classical solutions to the $q$-Painlev\'e equation of type $(A_1+A_1')^{(1)}$ (a $q$-difference analog of the Painlev\'e II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this $q$-Painlev\'e equation to the Painlev\'e 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. 
Taro Hamamoto, Kenji Kajiwara and Nicholas S. Witte