nLab resummation

Idea

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.

• Borel resummation

Related concepts

• perturbation theory

• resurgence

References

The main historical reference is the monograph of Hardy, still very readable (and of course, accurate).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

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

More recent developments include

• Ovidiu Costin, Gerald V. Dunne, Convergence from Divergence (arXiv:1705.09687)