Cesàro Summation
Cesàro Summation
The Cesàro sum of an infinite series is given by , provided that this limit exists. If a convergent series has sum , then it is Cesàro summable and has Cesàro sum . A divergent series may still have a well-defined Cesàro sum. This Demonstration considers the series sin(k), which is classically divergent but has the Cesàro sum cot.
∞
∑
k=0
f
k
lim
m∞
1
m+1
m
∑
n=0
n
∑
k=0
f
k
S
S
∞
∑
k=0
1
2
1
2