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Asymptotic formulae of two divergent bilateral basic hypergeometric series (1611.04663v1)
Published 15 Nov 2016 in math.CA, hep-th, math-ph, and math.MP
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.
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