q-Stokes Phenomenon of a Basic Hypergeometric Series 1ϕ1(0; a; q, x)

We show a connection formula of a linear q-differential equation satisfied by 1ϕ1(0; a; q, x). The basic hypergeometric series 1ϕ1(0; a; q, x) represents the Hahn-Exton q-Bessel function. Since the q-differential equation has a divergent series solution, a q-analogue of the Stokes phenomenon appears. We give a resummation procedure of the divergent series by means of the q-Borel-Laplace transformation of order 1/2.