Cesàro summation [SEP] named after
Cesàro summation
In mathematical analysis, Cesàro summation (also known as the Cesàro mean) assigns values to some infinite sums that are not convergent in the usual sense. The Cesàro sum is defined as the limit, as "n" tends to infinity, of the sequence of arithmetic means of the first "n" partial sums of the series.
Cesàro summation is named for the Italian analyst Ernesto Cesàro (1859–1906). It is a special case of a matrix summability method.
The term "summation" can
Fejér kernel
In mathematics, the Fejér kernel is a summability kernel used to express the effect of Cesàro summation on Fourier series. It is a non-negative kernel, giving rise to an approximate identity. It is named after the Hungarian mathematician Lipót Fejér (1880–1959).
Definition.
The Fejér kernel is defined as 
where 
is the "k"th order Dirichlet kernel. It can also be written in a closed form as
where this expression is defined. 
The Fejér kernel can also be expressed as