Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633331 | Applied Mathematics and Computation | 2009 | 24 Pages |
Abstract
A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn's epsilon algorithm, Weniger transformation [E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Computer Physics Reports 10 (1989) 189-371] or the technique recently introduced by ÄÞek et al. [J. ÄÞek, J. Zamastil, L. Skála, New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field, Journal of Mathematical Physics 44 (3) (2003) 962-968]. In the case of trigonometric series, our method is very similar to the Homeier's H transformation, while in the case of orthogonal series - to the K transformation. Two iterated methods related to the proposed method are considered. Some theoretical results and several illustrative numerical examples are given.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
PaweŠWoźny, RafaŠNowak,