Interplay Between Generalized Functions and the Theory of Moments
Estrada and Kanwal have recently [6, 69–71] developed a distributional approach to asymptotic analysis. Their study is based on the interplay between the generalized functions and the theory of moments. Thus, they have not only succeeded in presenting a simplified approach to various known aspects of asymptotics but have also found many new results. They have applied their technique to many different branches of asymptotic expansions, such as asymptotic evaluation of divergent integrals, boundary layer theory and singular perturbations. Our aim in this chapter is to present the basic concepts of their methods and illustrate them with representative examples.
KeywordsWeight Function Asymptotic Expansion Orthogonal Polynomial Boundary Layer Theory Distributional Approach
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