Cesàro summation

In mathematical analysis, Cesàro summation is an alternative means of assigning a sum to an infinite series.

One summability method, popular in Fourier analysis, is that of Cesàro summation.

The Abel sum is therefore regular, linear, stable, and consistent with Cesàro summation.

Two of the simplest methods are Cesàro summation and Abel summation.

Cesàro summation is an averaging method, in that it relies on the arithmetic mean of the sequence of partial sums.

In mathematics, the Fejér kernel is used to express the effect of Cesàro summation on Fourier series.

C is ordinary summation, and C is ordinary Cesàro summation.

For example, Fejér's theorem shows that if one replaces ordinary summation by Cesàro summation then the Fourier series of any continuous function converges pointwise everywhere to the function.

Summability methods include Cesàro summation, (C,k) summation, Abel summation, and Borel summation, in increasing order of generality (and hence applicable to increasingly divergent series).

Aksel Frederik Andersen (10 February 1891 Fodby, Denmark - 1972 Gentofte, Denmark) was a Danish mathematician who worked on infinite series and in particular on Cesàro summation.

The subject of divergent series, as a domain of mathematical analysis, is primarily concerned with explicit and natural techniques such as Abel summation, Cesàro summation and Borel summation, and their relationships.