### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 115, 11 pages      arXiv:1105.1998      https://doi.org/10.3842/SIGMA.2011.115

### 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

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

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→1 of the connection formula.

Key words: Hahn-Exton q-Bessel function; q-Borel transformation; connection problems.

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