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140122 ||| eng |
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|a 9781468400298
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| 100 |
1 |
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|a Estrada, Ricardo
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| 245 |
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|a Asymptotic Analysis
|h Elektronische Ressource
|b A Distributional Approach
|c by Ricardo Estrada, Ram P. Kanwal
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| 250 |
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|a 1st ed. 1994
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| 260 |
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|a Boston, MA
|b Birkhäuser
|c 1994, 1994
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| 300 |
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|a IX, 258 p
|b online resource
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| 505 |
0 |
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|a 1 Basic Results in Asymptotics -- 1.1 Introduction -- 1.2 Order Symbols -- 1.3 Asymptotic Series -- 1.4 Algebraic and Analytic Operations -- 1.5 Existence of Functions with a Given Asymptotic Expansion -- 1.6 Asymptotic Power Series in a Complex Variable -- 1.7 Asymptotic Approximation of Partial Sums -- 1.8 The Euler-Maclaurin Summation Formula -- 2 Introduction to the Theory of Distributions -- 2.1 Introduction -- 2.2 The Space of Distributions
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| 653 |
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|a Approximations and Expansions
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| 653 |
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|a Probability Theory
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| 653 |
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|a Approximation theory
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| 653 |
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|a Probabilities
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| 700 |
1 |
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|a Kanwal, Ram P.
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 028 |
5 |
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|a 10.1007/978-1-4684-0029-8
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4684-0029-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 511.4
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| 520 |
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|a Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature
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