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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.
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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