This article is cited in 6 papers

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

Takeshi Morita

Graduate School of Information Science and Technology, Osaka University, 1-1 Machikaneyama-machi, Toyonaka, 560-0043, Japan

Abstract: 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, $q$-Borel transformation, connection problems.

MSC: 33D15; 34M40; 39A13

Received: May 11, 2011; in final form December 14, 2011; Published online December 16, 2011

Language: English

DOI: 10.3842/SIGMA.2011.115

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ArXiv: 1105.1998