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The Petersson-Kuznetsov trace formula is a basic tool in the analytic study of GL(2) L-functions. One main obstacle in applying it to higher-rank groups is the lack of knowledge about the integral transforms on the geometric side. It was first observed by Cogdell and Piatetski-Shapiro that the kernel functions of these integral transforms are Bessel functions defined from the perspective of local representation theory. We will explain this view with GL(2) and then show a general way to compute Bessel functions on GL(n). Specifically, for Bessel functions on GL(3), our method leads to uniform asymptotic expansions of the associated integral transforms, which are crucial for the more subtle application of the GL(3) Kuznetsov formula such as subconvexity.