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 Gamma(alpha, x; b) = integral(x)(infinity)t(alpha-1)e(-t-b/t)dt, x > 0, Re b greater than or equal to 0, b not equal 0, as x tends to infinity, where the real paramete alpha is allowed to take negative values. In the case b = -i omega, omega > 0, we obtain the expansions of the decomposition functions C-Gamma(alpha, x; omega) and S-Gamma(alpha,x; omega). Closed form expressions are also given for alpha = -3/2, -5/2, ... (C) Academic Press.