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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. (English) Zbl 0928.34039

Summary: The author examines the resurgence properties of the coefficients c r (η) appearing in a uniform asymptotic expansion of the incomplete gamma function. For the coefficients c r (η), he gives an asymptotic approximation as r that is a sum of two incomplete beta functions plus a simple asymptotic series in which the coefficients are again c m (η).

The method is based on the Borel-Laplace transform, which means that next to the asymptotic approximation of c r (η), one obtains an exponentially-improved asymptotic expansion for the incomplete gamma function.

MSC:
34E05Asymptotic expansions (ODE)
33B20Incomplete beta and gamma functions