resummation

A **resummation** is an operation which applies to some class of series and which makes some divergent series become convergent. Normally one requires that the operation makes sense also to the series which are convergent to start with and then the resummation gives a series with the same sum as the original one.

The main historical reference is the monograph of Hardy, still very readable (and of course, accurate).

- G. H. Hardy,
*Divergent series*, Clarendon Press, Oxford, 1949.

Some resummation methods can be made sense also from the point of view of nonstandard analysis.

- Vladimir Kanovei, Michael Reeken,
*Summation of divergent series from the nonstandard piont of view*, Real Anal. Exchange**21**:2 (1995) 473-497 euclid

Revised on September 18, 2016 08:40:21
by Zoran Škoda
(37.244.136.105)