Abstract

The generalised Euler transformation is a well-known device for accelerating the numerical convergence of infinite series. In practice the transformation is often applied to the infinite series remaining after the first m terms have been added together to form a partial sum. The other partial sums, obtained by taking the first m terms of the original series and the first r terms of the transformed remained series form a double sequence of approximations to the sum or formal sum of the original series. The purpose of this note is to point out that the partial sums may be built up by means of a remarkably simple recursion.

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