Watson's Lemma with applications.

Abstract

This thesis is about Watson's Lemma. This lemma describes the behavior of the Laplace and Laplace-Stieltjes integrals near infinity. Consequently, we can use this lemma to find asymptotic expansions of functions that can be written in the Laplace or Laplace-Stieltjes integral form. This study is mainly based on the Riemann-Stieltjes and Laplace-Stieltjes integrals.