Stolarsky mean


In mathematics, the Stolarsky mean is a generalization of the logarithmic mean. It was introduced by Kenneth B. Stolarsky in 1975.

Definition

For two positive real numbers x, y the Stolarsky Mean is defined as:

Derivation

It is derived from the mean value theorem, which states that a secant line, cutting the graph of a differentiable function at and, has the same slope as a line tangent to the graph at some point in the interval.
The Stolarsky mean is obtained by
when choosing.

Special cases

One can generalize the mean to n + 1 variables by considering the mean value theorem for divided differences for the nth derivative.
One obtains