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Analysis Mathematica

, Volume 33, Issue 3, pp 161–198 | Cite as

Polynomial asymptotic expansions in the real domain: the geometric, the factorizational, and the stabilization approaches

  • Antonio Granata
Article

Abstract

The problem of the existence of an asymptotic expansion of type
$$ f(x) = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_i x^i + o(x^i ), x \to + \infty , $$
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.

Keywords

Asymptotic Expansion Integral Condition Russian Mathematician Soviet Math Asymptotic Relation 
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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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Antonio Granata
    • 1
  1. 1.Dipartimento di MatematicaUniversita’ Della CalabriaRende (Cosenza)Italy

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