Bucurel Minea and Eugen Paltanea: Laplace's method for the case of a countably infinite set of global maximum points, p.81-94

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.

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