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Logarithmic summation method

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One of the methods for summing series of numbers. A series with partial sums is summable by the logarithmic method to the sum if the logarithmic mean

converges to as . The logarithmic summation method is the Riesz summation method with . It is equivalent to and compatible (cf. Compatibility of summation methods) with the Riesz summation method with and is more powerful than the summation method of arithmetical averages (cf. Arithmetical averages, summation method of).

References

[1] F. Riesz, "Sur la sommation des séries de Dirichlet" C.R. Acad. Sci. Paris , 149 (1909) pp. 18–21
[2] G.H. Hardy, "Divergent series" , Clarendon Press (1949)
How to Cite This Entry:
Logarithmic summation method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Logarithmic_summation_method&oldid=32663
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article