关于对称函数E_r的不等式

Inequality of Symmetric Function

从几个非负实数中任取r个不同者相乘,把所有可能乘积的和记为ē_r,又记ē_r=E_r/C_n^r,本文的目的在于证明:ē_r^2≥ē_(r-1)·ē_(r+1)。

Let x_1, x_2, …', x_n, be non-negative real numbers. ē_r is defined by: ē_r=(C_n^r)^(-1) sum from i_1<i_2<…<i_r(x_(i_1)x_(i_2)…x_(i_r). In this paper, we have proved that ē_r satisfies: ē_r^2≥ē_(r-1)·ē_(r+1).