Asymptotic formulae of two divergent bilateral basic hypergeometric series

Abstract

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 ${}_1{\psi }_1(a;b;q,z)$. Moreover, we show that our formulae have the $q\to 1-0$ limit.

13 pages

References in corpus (2)

• Algebraic construction of the Stokes sheaf for irregular linear q-difference equations
• On local solutions of the Ramanujan equation and their connection formulae