Stolarsky mean

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