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Effective Summation and Interpolation of Series by Self-Similar Root Approximants

Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
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Academic Editor: Palle E. T. Jorgensen
Mathematics 2015, 3(2), 510-526; https://doi.org/10.3390/math3020510
Received: 25 March 2015 / Accepted: 9 June 2015 / Published: 15 June 2015
(This article belongs to the Special Issue Mathematical physics)
We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined. View Full-Text
Keywords: asymptotic series; effective summation; root approximants; self-similar approximation theory asymptotic series; effective summation; root approximants; self-similar approximation theory
MDPI and ACS Style

Gluzman, S.; Yukalov, V.I. Effective Summation and Interpolation of Series by Self-Similar Root Approximants. Mathematics 2015, 3, 510-526. https://doi.org/10.3390/math3020510

AMA Style

Gluzman S, Yukalov VI. Effective Summation and Interpolation of Series by Self-Similar Root Approximants. Mathematics. 2015; 3(2):510-526. https://doi.org/10.3390/math3020510

Chicago/Turabian Style

Gluzman, Simon; Yukalov, Vyacheslav I. 2015. "Effective Summation and Interpolation of Series by Self-Similar Root Approximants" Mathematics 3, no. 2: 510-526. https://doi.org/10.3390/math3020510

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