Abstract
In this paper, an acceleration technique based on a Kummer’s transformation method is developed for some slowly convergent series. The original series is decomposed into two parts; one part being rapidly convergent and the other part being slowly convergent. Then the series in the slowly convergent part is expressed as integrals of some auxiliary functions and subsequently they are written in terms of polynomials whose coefficients are given by the zeta functions. The given method is computationally oriented and does not involve much analytic effort. A numerical example is provided to illustrate the usage and the efficiency of the method.
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References
A. Uzer T. Ege (2003) ArticleTitleAn improved convergence acceleration method for the strip grating cylindrical surface problem Electr. Engng. 86 55–60
M. Abbromowitz I. A. Stegun (1965) Handbook of mathematical functions Dover Washington, D.C
Flajolet, P., Vardi, I.: Zeta function expansions of classical constants. (1996) Unpublished memo, available online http://pauillac.inria.fr/algo/flajolet/publications.
R. E. Collin (1991) Field theory of guided waves IEEE Press New York
H. H. H. Homeier (2000) ArticleTitleScalar Levin-type sequence transformations Invited Rev. J. Comput. Appl. Math. 122 81–147 Occurrence Handle10.1016/S0377-0427(00)00359-9
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Uzer, A., Ege, T. On the Convergence Acceleration of Slowly Convergent Sums Involving Oscillating Terms. Computing 75, 311–318 (2005). https://doi.org/10.1007/s00607-005-0126-2
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DOI: https://doi.org/10.1007/s00607-005-0126-2