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

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

2011-04-05

arxiv.org/abs/1104.0755v2

Mathematics

Classical Analysis and ODEs

Scientific paper

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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