Asymptotic formulae of two divergent bilateral basic hypergeometric series

We provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1{\psi }_1(a;b;q,z)$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection formulae of $q$-difference equation for ${}_1\psi_1 ( a; b; q, z )$\mathrm{.}Moreover,weshowthatourformulaehavethe$q \to 1 - 0$ limit.