Cesàro mean


Let {an}n=0 be a sequence of real (or possibly complex numbersMathworldPlanetmathPlanetmath). The Cesàro mean of the sequence {an} is the sequence {bn}n=0 with

bn=1n+1i=0nai. (1)

0.0.1 Properties

  1. 1.

    A key property of the Cesàro mean is that it has the same limit as the original sequence (when this limit exists). In other words, if {an} and {bn} are as above, and ana, then bna. In particular, if {an} converges, then {bn} converges too.

Title Cesàro mean
Canonical name CesaroMean
Date of creation 2013-03-22 12:29:54
Last modified on 2013-03-22 12:29:54
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Definition
Classification msc 40-00
Classification msc 40G05
Synonym Cesaro mean
Related topic Sequence
Related topic CesaroSummability
Related topic StolzCesaroTheorem