Limiting relationships and comparison theorems for sequences
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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.
KeywordsAsymptotic Expansion Relative Rate Relative Order Mathematical Concept Comparison Theorem
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- Aitken A. C.,On Bernouilli's numerical solution of algebraic equations. Proc. Roy. Soc. Edinburgh,46 (1926), 289–305.Google Scholar
- Bourbaki N.,Fonction d'une variable réelle, livre 4, chapitre 5. Hermann, Paris, 1951.Google Scholar
- Bromwich, T. J.,An introduction to the theory of infinite series. Macmillan, London, 2d ed. 1949.Google Scholar
- Clark W. D.,Infinite series transformations and their applications. Thesis, Univ. of Texas, 1967.Google Scholar