On the Approximation of a Generalized Incomplete Gamma Function Arising in Heat Conduction Problems

Several asymptotic expansions are given for the generalized incomplete gamma function Ž , x; b. Hx t 1e t b tdt, x 0, Re b 0, b 0, as x tends to infinity, where the real parameter is allowed to take negative values. In the case b i , 0, we obtain the expansions of the decomposition functions C Ž , x; .and S Ž , x; .. Closed form expressions are also given for 3 2, 5 2, . . . .