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arXiv · 1402.3903

The Stokes phenomenon for the $q$-difference equation satisfied by the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$

Takeshi Morita
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Abstract

We show the connection formula for the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$ between around the origin and infinity by the using of the $q$-Borel-Laplace transformations. We also show the limit $q\to 1-0$ of the new connection formula.

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Takeshi Morita. 2014-02-17. The Stokes phenomenon for the $q$-difference equation satisfied by the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$. https://arxiv.org/abs/1402.3903

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