For two positive real numbers x, y the Stolarsky Mean is defined as:
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 .
- is the minimum.
- is the geometric mean.
- is the logarithmic mean. It can be obtained from the mean value theorem by choosing .
- is the power mean with exponent .
- is the identric mean. It can be obtained from the mean value theorem by choosing .
- is the arithmetic mean.
- is a connection to the quadratic mean and the geometric mean.
- is the maximum.
One can generalize the mean to n + 1 variables by considering the mean value theorem for divided differences for the nth derivative.
- for .