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 duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
s ''x'', ''y'' is defined as:
:
It can be derived from the
mean value theorem
In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc (geometry), arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant lin ...
by considering the
secant of the graph of the function
. It can be generalized to more variables according by the
mean value theorem for divided differences. The identric mean is a special case of the
Stolarsky mean.
See also
*
Mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...
*
Logarithmic mean
References
*
{{DEFAULTSORT:Identric Mean
Means