Hölder summation - Alchetron, The Free Social Encyclopedia

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

Definition

Given a series

a 1 + a 2 + ⋯ ,

define

H n 0 = a 1 + a 2 + ⋯ + a n H n k + 1 = H 1 k + ⋯ + H n k n

If the limit

lim n → ∞ H n k

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

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