Nörlund mean

Summary

A Nörlund mean is a weighted average of the first terms of a sequence. Its weights are read backwards from a fixed sequence $p_0, p_1, p_2, \dots$. It defines a summability method for sequences and, through partial sums, for series. With all weights equal to $1$ it is the Cesàro mean. The method gives the usual limit to every convergent sequence exactly when $p_n$ is small compared with $p_0 + \cdots + p_n$.