Hölder summation

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In mathematics, Hölder summation is a method for summing divergent series introduced by Hölder (1882).

Definition[edit]

Given a series

 a_1+a_2+\cdots, \,

define

H^0_n=a_1+a_2+\cdots+a_n \,
H^{k+1}_n=\frac{H^k_1+\cdots+H^k_n}{n}

If the limit

\lim_{n\rightarrow\infty}H^k_n \,

exists for some k, this is called the Hölder sum, or the (H,k) sum, of the series.

References[edit]