Hölder summation

Summary

Hölder summation is a summability method that averages the partial sums of a series, then averages these averages. It repeats the averaging a fixed number $k$ of times. For $k = 1$ it is Cesàro summation of order $1$. For each $k$, the Hölder method of order $k$ sums the same series to the same values as the Cesàro method of order $k$. Repeated averaging can tame series whose partial sums oscillate with growing size.