- Identric mean
The Identric mean of two positive
real number s x,y is defined as: :egin{matrix}I(x,y)&=&frac{1}{e}cdotlim_{(xi,eta) o(x,y)}sqrt [xi-eta] {frac{xi^xi}{eta^eta\&=&lim_{(xi,eta) o(x,y)}expleft(frac{xicdotlnxi-etacdotlneta}{xi-eta}-1 ight)\&=&egin{cases}x & mbox{if }x=y \frac{1}{e} sqrt [x-y] {frac{x^x}{y^y & mbox{else}end{cases}end{matrix}.It can be derived from the
mean value theorem by considering the secant of the graph of the function x mapsto xcdot ln x. It can be generalized to more variables according by themean value theorem for divided differences .ee also
* The identric mean is a special case of the
Stolarsky mean .
*Mean
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