Abstract
In this chapter, we present the general theory of ca se s: their definition and their behavior with respect to the basic operations of addition, multiplication, division, differentiation, integration, composition and analytic continuation. We also link our ca se s to the inner and outer expansions of the classical method of matching. Using these inner and outer expansions is also a good method for determining the coefficients of a composite expansion in practice, provided one can show the existence of a composite expansion independently.
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Fruchard, A., Schäfke, R. (2013). Composite Asymptotic Expansions: General Study. In: Composite Asymptotic Expansions. Lecture Notes in Mathematics, vol 2066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34035-2_2
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