Namespaces
Variants
Actions

Arithmetical averages, summation method of

From Encyclopedia of Mathematics
Revision as of 17:26, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

One of the methods for summing series and sequences. The series

is summable by the method of arithmetical averages to the sum if

where . In this case, one also says that the sequence is summable by the method of arithmetical averages to the limit . The summation method of arithmetical averages is also called the Cesàro summation method of the first order (cf. Cesàro summation methods). The summation method of arithmetical averages is completely regular (see Regular summation methods) and translative (see Translativity of a summation method).

References

[1] G.H. Hardy, "Divergent series" , Clarendon Press (1949)


Comments

Instead of "arithmetical averages" the term "summation method of arithmetical meansarithmetical means" is sometimes used, cf. [a1], and instead of "summation" one also uses "summability" : summability method.

References

[a1] R.G. Cooke, "Infinite matrices and sequence spaces" , Macmillan (1950)
How to Cite This Entry:
Arithmetical averages, summation method of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Arithmetical_averages,_summation_method_of&oldid=18557
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article