Lehmer mean
In mathematics, the Lehmer mean of a tuple x {\displaystyle x} of positive real numbers, named after Derrick Henry Lehmer, is defined as: L p ( x ) = ∑ k = 1 n x k p ∑ k = 1 n x k p − 1 . {\displaystyle L_{p}(\mathbf {x} )={\frac {\sum _{k=1}^{n}x_{k}^{p}}{\sum _{k=1}^{n}x_{k}^{p-1}}}.} The weighted Lehmer mean with respect to a tuple w {\displaystyle w} of positive weights is defined as: L p , w ( x ) = ∑ k = 1 n w k ⋅ x k p ∑ k = 1 n w k ⋅ x k p − 1 .