an:01310572
Zbl 0928.34039
Olde Daalhuis, A. B.
On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function
EN
Methods Appl. Anal. 5, No. 4, 425-438 (1998).
00055922
1998
j
34E05 33B20
incomplete gamma function; Borel-Laplace transform
Summary: The author examines the resurgence properties of the coefficients \(c_r(\eta)\) appearing in a uniform asymptotic expansion of the incomplete gamma function. For the coefficients \(c_r(\eta)\), he gives an asymptotic approximation as \(r\to\infty\) that is a sum of two incomplete beta functions plus a simple asymptotic series in which the coefficients are again \(c_m(\eta)\).
The method is based on the Borel-Laplace transform, which means that next to the asymptotic approximation of \(c_r(\eta)\), one obtains an exponentially-improved asymptotic expansion for the incomplete gamma function.