The Stokes phenomenon for the Ramanujan's q-difference equation and its higher order extension

Original · EN

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 ₂φ₀(0,0;-;q,x). We use two different q-Borel-Laplace resummation methods to obtain our connection formulae. We also introduce the q-Borel-Laplace transformation of level r-1, which are higher order extension of these transformations. These methods are useful to obtain an asymptotic formula of a divergent series ᵣφ₀(0,0,,0;-;q,x).