Paper Title:

Using an Euler Type Transform for Accelerating Convergence of Series

Author(s):

Nimete Sh. Berisha, Faton M. Berisha^*, Murat Sadiku

Faculty of Economics, University of Prishtina,
Agim Ramadani st., 10000 Pristina,
Kosovo.
E-mail: nimete.berisha@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/nimeteberisha

Faculty of Mathematics and Sciences, University of Prishtina,
Mother Teresa st., 10000 Pristina,
Kosovo.
E-mail: faton.berisha@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/fatonberisha

Faculty of Business Administration,
South East European University,
Tetovo,
North Macedonia.
E-mail: m.sadiku@seeu.edu.mk

Abstract:

In the paper we give a property of an operator of generalised difference, defined earlier, linear on a set of sequences, and use it to establish Euler type transforms for alternating series. These transforms accelerate the convergence of series under the same conditions as the transforms of non-alternating series. We also give analysis of an algorithm for computing a partial sum of the transformed series by using a higher order operator of generalised difference, and prove a theorem stating its order of complexity.

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