Hölder Summation

In mathematics, Hölder summation is a method for summing divergent series introduced by .

Definition

Given a series
:$a_1+a_2+\cdots,$
define
:$H^0_n=a_1+a_2+\cdots+a_n$
:$H^_n=\frac$
If the limit
:$\lim_H^k_n$
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:

:$\lim_H^k_n$

See also

* Cesàro summation

References

*
*

Summability methods
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