Abstract:
We propose an extension of the well-known method of Laplace which provides the asymptotic expansion of exponential integrals. We study the situation where the corresponding exponent is a function with a countably infinite set of global maximum points. We establish conditions for a certain asymptotic behaviour of this kind of integrals. Finally, we illustrate the theoretical results with two examples.
Key Words: Exponential integral, asymptotic behaviour, Laplace's method, Watson's lemma.
2010 Mathematics Subject Classification: Primary: 41A60;
Secondary: 40A05, 26A42.
Download the paper in pdf format here.