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: 
formula_1
Derivation.
It is derived from the mean value theorem, which states that a secant line, cutting the graph of a differentiable function formula_2 at formula_3 and formula_4, has the same slope as a line tangent to the graph at some point formula_5 in the interval formula_6.
formula_7
The Stolarsky mean is obtained by
formula_8
when choosing formula_9.
Generalizations.
One can generalize the mean to "n" + 1 variables by considering the mean value theorem for divided differences for the "n"th derivative.
One obtains
formula_21 for formula_22.
References.
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