


Paper's 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.
Email: nimete.berisha@unipr.edu
URL:
https://staff.unipr.edu/profile/nimeteberisha
Faculty of Mathematics and Sciences,
University of Prishtina,
Mother Teresa st., 10000 Pristina,
Kosovo.
Email: faton.berisha@unipr.edu
URL:
https://staff.unipr.edu/profile/fatonberisha
Faculty of Business Administration,
South East European University,
Tetovo,
North Macedonia.
Email: 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 nonalternating 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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