Limiting relationships and comparison theorems for sequences |
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Authors: | Claude Brezinski |
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Affiliation: | 1. Université S. et T. Lille, UER d'I.E.E.A. Informatique, 59655, Villeneuve d'Ascq Cedex, Francia
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Abstract: | 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. |
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