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Kummer transformation

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A transformation of series of numbers which improves the convergence; proposed by E. Kummer. Let

be convergent series and let the limit

exist. Then

If the sum is known, the Kummer transformation may prove useful in computations, since the series on the right converges more rapidly than that on the left.

References

[1] G.M. Fichtenholz, "Differential und Integralrechnung" , 2 , Deutsch. Verlag Wissenschaft. (1964)


Comments

References

[a1] K. Knopp, "Infinite sequences and series" , Dover, reprint (1956) (Translated from German)
How to Cite This Entry:
Kummer transformation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kummer_transformation&oldid=17267
This article was adapted from an original article by V.V. Senatov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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