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.
One obtains
for
.