Abstract
The preceding sections illustrated the use of 7 important tools of nonstandard asymptotic analysis:
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1)
External sets and relations
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2)
Permanence principles
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3)
The classification of convex external subsets of ℝ
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4)
The lemma of dominated approximation
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5)
The concentration lemma
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6)
The Laplace method with parameters
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7)
Shadow expansions In Chapters II and III we attempt to embed the examples of this chapter into a general theory of approximation. Chapters IV, V and VI are devoted to the tools.
Keywords
- Asymptotic Expansion
- Small Term
- Nonstandard Analysis
- Taylor Polynomial
- Order Scale
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1987 Springer-Verlag
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van den Berg, I. (1987). Four examples of nonstandard reasoning in asymptotics. In: Nonstandard Asymptotic Analysis. Lecture Notes in Mathematics, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077578
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DOI: https://doi.org/10.1007/BFb0077578
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17767-8
Online ISBN: 978-3-540-47810-2
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