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Asymptotic behaviour of iterated modified 401-1401-1401-1401-2401-2401-2transforms on some slowly convergent sequences

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Abstract

LetL(α, r) denote the class of complex sequences (x n) having an asymptotic expansion of type

$$x_n \sim \sum\limits_{i \ge 0} {c_i n^{ - (\alpha + ri)} } , c_0 \ne 0,\alpha > 0,r > 0.$$

We describe the asymptotic behaviour of sequences obtained by applying to (x n) some specific modified versions of the iterated Δ2 transform, the θ2 transform and some combinations of them. In this paper, we study the particular casesr=1 andr=1/2, which are the most useful in practice. The results are also valid for sequences (S n) whose error sequence (x n) defined byx n=S n−S, S=limS n, belongs to someL(α, r).

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  1. Laboratoire LANS, Institut National des Sciences Appliquées, 20, avenue des Buttes de Coësmes, 35043, Rennes Cédex, France

    Paul Sablonnière

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  1. Paul Sablonnière
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Sablonnière, P. Asymptotic behaviour of iterated modified 401-1401-1401-1401-2401-2401-2transforms on some slowly convergent sequences. Numer Algor 3, 401–409 (1992). https://doi.org/10.1007/BF02141947

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  • DOI: https://doi.org/10.1007/BF02141947

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