Hölder summation
In mathematics, Hölder summation is a method for summing divergent series introduced by Hölder (1882). == Definition == Given a series a 1 + a 2 + ⋯ , {\displaystyle a_{1}+a_{2}+\cdots ,} define H n 0 = a 1 + a 2 + ⋯ + a n {\displaystyle H_{n}^{0}=a_{1}+a_{2}+\cdots +a_{n}} H n k + 1 = H 1 k + ⋯ + H n k n {\displaystyle H_{n}^{k+1}={\frac {H_{1}^{k}+\cdots +H_{n}^{k}}{n}}} If the limit lim n → ∞ H n k {\displaystyle \lim _{n\rightarrow \infty }H_{n}^{k}} exists for some k, this is called the Hölder sum, or the (H,k) sum, of the series.