WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Cesàro Summation

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

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.