The identric mean of two positive

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s ''x'', ''y'' is defined as: :

& \text \end \end

It can be derived from the

mean value theorem In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It i ...

by considering the secant of the graph of the function

x \mapsto x\cdot \ln x

. It can be generalized to more variables according by the

mean value theorem for divided differences In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. Statement of the theorem For any ''n'' + 1 pairwise distinct points ''x''0, ..., ''x'n'' in ...

. The identric mean is a special case of the

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: : \begin S_p(x,y) & = ...

References

{{DEFAULTSORT:Identric Mean Means

See also

References