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  • 1 Universita’ Della Calabria Dipartimento di Matematica 87036 Rende (Cosenza) Italy
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Abstract  

The problem of the existence of an asymptotic expansion of type

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$f(x) = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_i x^i + o(x^i ), x \to + \infty ,$$ \end{document}
is thoroughly studied, comparing and completing the known results obtained through the three different approaches mentioned in the title. A unifying thread is provided by the canonical factorizations of the differential operator D n. Particularly meaningful are several characterizations of the polynomial asymptotic expansions of an nth order convex function.

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