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We examine the resurgence properties of the coefficients 07.(77) appearing in the uniform asymptotic expansion of the incomplete gamma function. For the coefficients cr(T7), we give an asymptotic approximation as r -» 00 that is a sum of two incomplete beta functions plus a simple asymptotic series in which the coefficients are again Cm(rj). The method of this paper is based on the Borel-Laplace transform, which means that next to the asymptotic approximation of CrC??), we also obtain an exponentially-improved asymptotic expansion for the incomplete gamma function.

On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function