The problem of differentiating an asymptotic expansion in real powers. I: Unsatisfactory or partial results by classical approaches
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.
differentiation of asymptotic expansions
scientific article; zbMATH DE number 5848629