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arXiv · 1203.3404

On local solutions of the Ramanujan equation and their connection formulae

Takeshi Morita
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Abstract

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series ${}_2\varphi_0(0,0;-;q,x)$. We use two different $q$-Borel-Laplace transformations to obtain our connection formulae.

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Takeshi Morita. 2012-03-15. On local solutions of the Ramanujan equation and their connection formulae. https://arxiv.org/abs/1203.3404

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