Gronwall summation method

From Encyclopedia of Mathematics
Revision as of 16:58, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A method for summing series of numbers or functions, defined by specifying two functions and satisfying certain conditions. A series can be summed by the Gronwall method to a sum if

where , is defined by the expansion

The method was introduced by T.H. Gronwall [1] as a generalization of the de la Vallée-Poussin summation method, to which it is converted by


then the Gronwall summation method becomes one of the Cesàro summation methods.


[1] T.H. Gronwall, "Summation of series and conformal mapping" Ann. of Math. , 33 : 1 (1932) pp. 101–117
How to Cite This Entry:
Gronwall summation method. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article