Hölder summation
In mathematics, Hölder summation is a method for summing divergent series introduced by Hölder (1882).
Definition
Given a series
define
If the limit
exists for some k, this is called the Hölder sum, or the (H,k) sum, of the series.
Particularly, since the Cesàro sum of a convergent series always exists, the Hölder sum of a series (that is Hölder summable) can be written in the following form:
See also
References
- Hölder, O. (1882), "Grenzwerthe von Reihen an der Konvergenzgrenze" (PDF), Math. Ann., 20: 535–549, doi:10.1007/bf01540142
- "Hölder summation methods", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
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