A Connection Formula of the Hahn-Exton $q$-Bessel Function

Details A Connection Formula of the Hahn-Exton $q$-Bessel Function A Connection Formula of the Hahn-Exton $q$-Bessel Function

2011-05-10

arxiv.org/abs/1105.1998v3

SIGMA 7 (2011), 115, 11 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2011.115

We show a connection formula of the Hahn-Exton $q$-Bessel function around the
origin and the infinity. We introduce the $q$-Borel transformation and the
$q$-Laplace transformation following C. Zhang to obtain the connection formula.
We consider the limit $p\to 1^-$ of the connection formula.

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