Elementary symmetric mean

Elementary symmetric mean

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

pecial cases

*M_1(x) is the arithmetic mean.
*M_n(x) is the geometric mean.

ee also

*The elementarsymmetric means are similar to a-means.

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