# Elementary symmetric mean

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Elementary symmetric mean

The elementary symmetric mean is based on elementary symmetric polynomials.If $x$ is a tuple with $x = \left(x_1,dots,x_n\right)$ and$alpha_p\left(x\right)$ is the corresponding elementary symmetric term of order $p$,then the respective mean is:$M_p\left(x\right) = sqrt \left[p\right] \left\{frac\left\{alpha_p\left(x\right)\right\}$n choose p}.

pecial cases

*$M_1\left(x\right)$ is the arithmetic mean.
*$M_n\left(x\right)$ is the geometric mean.

ee also

*The elementarsymmetric means are similar to a-means.
*mean

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