Limiting relationships and comparison theorems for sequences

  • Claude Brezinski


The aim of this paper is to define some mathematical concepts which are useful to measure the speed of convergence of a sequence and to compare two converging sequences. In that way we define the order, the relative order and the α-equivalence of sequences. The asymptotic expansion of a series is studied and an application to Aitken acceleration process is given. A theorem similar to l'Hospital's rule is also proved for sequences.


Asymptotic Expansion Relative Rate Relative Order Mathematical Concept Comparison Theorem 
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 1979

Authors and Affiliations

  • Claude Brezinski
    • 1
  1. 1.Université S. et T. LilleUER d'I.E.E.A. InformatiqueVilleneuve d'Ascq CedexFrancia

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