Geodesic
A Connection Formula of the Hahn–Exton $q$-Bessel Function
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Hahn–Exton $q$-Bessel function, connection problems.
Mots-clés : $q$-Borel transformation 
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     author = {Takeshi Morita},
     title = {A {Connection} {Formula} of the {Hahn{\textendash}Exton} $q${-Bessel} {Function}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a114/}
}
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Takeshi Morita. A Connection Formula of the Hahn–Exton $q$-Bessel Function. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a114/

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