The problem of differentiating an asymptotic expansion in real powers. I: Unsatisfactory or partial results by classical approaches (Q624255)
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scientific article; zbMATH DE number 5848629
| Language | Label | Description | Also known as |
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| English | The problem of differentiating an asymptotic expansion in real powers. I: Unsatisfactory or partial results by classical approaches |
scientific article; zbMATH DE number 5848629 |
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The problem of differentiating an asymptotic expansion in real powers. I: Unsatisfactory or partial results by classical approaches (English)
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8 February 2011
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The paper deals with the differentiation of real asymptotic expansions \(f(x)=\sum^n_{i=1} a_i x^{d_i}+O(x^\gamma)\) as \( x\to\infty\), and also of corresponding expansions with \(o\) instead of \(O\), under additional assumptions concerning \(f'\), \(f''\) or a second order differential operator of Euler type. Moreover, the possibility of higher differentiations is investigated. Examples show that some of the results are best possible.
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differentiation of asymptotic expansions
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