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arXiv · 1104.0755

A connection formula between the Ramanujan function and the $q$-Airy function

Takeshi Morita
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Abstract

We show a connection formula between two different $q$-Airy functions. One is called the Ramanujan function which appears in Ramanujan's "Lost notebook". Another one is called the $q$-Airy function that obtained in the study of the second $q$-Painlev\'e equation. We use the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula.

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Takeshi Morita. 2011-04-05. A connection formula between the Ramanujan function and the $q$-Airy function. https://arxiv.org/abs/1104.0755

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