Asymptotic formulae of two divergent bilateral basic hypergeometric series

2016/11/15 by Mori, Hironori, Morita, Takeshi
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1611.04663

Abstract

We provide new formulae for the degenerations of the bilateral basic hypergeometric function ₁ψ₁ ( 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 ₁ψ₁ ( a; b; q, z ). Moreover, we show that our formulae have the q → 1 - 0 limit.

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