Lehmer mean

In mathematics, the Lehmer - agent is a by Derrick Henry Lehmer named, generalized mean.

Definition

The Lehmer means of positive real numbers for the stage is defined as follows:

There is also a form of Lehmer means with (positive) weights. The weighted Lehmer means is:

Properties

For the Lehmer means

  • .
  • Is the harmonic mean.
  • Is the geometric mean of and.
  • Is the arithmetic mean.
  • .
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