Properties of the epsilon algorithm for convergent and divergent series

Date

1973

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Abstract

The purpose of this thesis is to investigate certain properties of the epsilon algorithm (also called the transformation T), in relation to convergent and divergent series. The transformation has been studied previously by Lubkin [1] and Shanks [2] both of whom were concerned with convergent series. This work extends the ideas concerning convergent series and includes results pertaining to divergent series. Whereas Lubkin and Shanks were concerned with the transform and its properties relative to faster convergence of series, the present work provides properties relating to uniformly and semi-uniformly faster convergence. Also, the idea of 'more slowly divergent series' is introduced and properties of the transform related to this idea are given with illustrative examples.

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Keywords

Transformations (Mathematics), Series, Divergent series

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