Lehmer mean

In mathematics, the Lehmer mean of a tuple ${\displaystyle x}$ of positive real numbers, named after Derrick Henry Lehmer, is defined as:

The weighted Lehmer mean with respect to a tuple ${\displaystyle w}$ of positive weights is defined as:

The Lehmer mean is an alternative to power means for interpolating between minimum and maximum via arithmetic mean and harmonic mean.

The derivative of ${\displaystyle p\mapsto L_{p}(x)}$ is non-negative

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