On local solutions of the Ramanujan equation and their connection formulae

Details On local solutions of the Ramanujan equation and their connection formulae On local solutions of the Ramanujan equation and their connection formulae

2012-03-15

arxiv.org/abs/1203.3404v1

Mathematics

Classical Analysis and ODEs

arXiv admin note: text overlap with arXiv:1104.0755

Scientific paper

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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