On local solutions of the Ramanujan equation and their connection   formulae
  We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series ${}_2\varphi_0(0,0;-;q,x)$. We use two different $q$-Borel-Laplace transformations to obtain our connection formulae. 
Takeshi Morita
math.CA