A Note on Uniform Asymptotic Expansion of Incomplete Laplace Integrals
Kusum Soni · SIAM Journal on Mathematical Analysis · 1983
An asymptotic expansion of the integral $F(z,a) = \int_a^\infty {e^{ - z(t - a)} } t^{\lambda - 1} g(t)dt,z \to \infty $, which is valid uniformly in $a \geq 0$, is obtained. The technique is elementary, and the expansion is simpler compared to those given earlier by Erdélyi [SIAM J. Math. Anal., 5 (1974), pp. 159–171] and Temme [SIAM J. Math. Anal., 7 (1976), pp. 767–770].