Cesáro summation

(redirected from Cesaro sum)

Cesáro summation

[chā′zä·rō sə′mā·shən]
(mathematics)
A method of attaching sums to certain divergent sequences and series by taking averages of the first n terms and passing to the limit.
References in periodicals archive ?
Summability techniques were also applied on some engineering problems; for example, Chen and Jeng [9] implemented the Cesaro sum of order (C, 1) and (C, 2), in order to accelerate the convergence rate to deal with the Gibbs phenomenon, for the dynamic response of a finite elastic body subjected to boundary traction.
Then nth partial sum [s.sub.n](x) of Fourier series (68) and nth Cesaro sum for [delta] = 1, that is, [[sigma].sup.1.sub.n] (x) for the series (68), are given by
We also show that if two double series are boundedly convergent, then the Cauchy product double series is Cesaro summable and its Cesaro sum is equal to the product of the sums of the given double series.
In that event, the above limit is called the Cesaro sum of the double series.
Then the Cauchy product double series [[SIGMA].sup.[infinity].sub.k,l = 0] [a.sub.k,l] * [b.sub.k, l] is Cesaro summable and its Cesaro sum is equal to AB, where A and B are the sums of the given double series.
The resulting series converges to 1/2, and this is called the 'Cesaro sum' of the original series.