IJPAM: Volume 50, No. 2 (2009)

THE ASYMPTOTIC ANALYSIS OF THE SEQUENCES

Andrei Vernescu$^1$, Cristinel Mortici$^2$
$^{1,2}$Department of Mathematics
University Valahia - Târgoviste
2, G. Enescu Str., Târgoviste, 130056, ROMANIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.We present here the principal problems of the asymptotic analysis of the sequences. These are: to find a simpler principal part for a divergent sequence or series, to obtain the speed of convergence for a convergent sequence or series by the first iterated limit or by a two sided estimation and finally to obtain an asymptotic expansion. Many of our results are remembered here.

Received: August 14, 2008

AMS Subject Classification: 26D15, 30B10, 33F05, 40A05, 40A60

Key Words and Phrases: sequence, limit of a sequence, series, sum of a series, convergence, speed of convergence, the symbols $O$ and $o$ of Landau, asymptotic expansion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2