Abstract
A Poisson-type integral representation for Jackson's q-Bessel function is obtained by using Askey and Wilson's q-beta integral and Nassrallah and Rahman's integral formula for an 8 ϑ 7 series. This representation along with some transformtion formulas for basic hypergeometric series help express the q-Bessel functions as a 3 ϑ 2 series in base q, a 2 ϑ 2 series in base q 2 and a 2 ϑ 1 series in base q q1 2 , where 0 < q < 1. As an application, q-analogues are found for Gegenbauer's degenerate addition formulas for Bessel functions.
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