与一类n元对称函数有关的几个恒等式以及一个对称不等式的初等证明

Several Identities on a Class of n-ary Symmetric Functions and an Elementary Proof of a Symmetric Inequality

设n∈N+,r∈N,a1,a2,…,an∈C,令E(r)n=E(r)n(a1,a2,…,an)=Σi1+i2+…+in=r ai11ai22…ainn,其中求和遍历使i1+i2+…+in=r的所有n元非负整数组(i1+i2+…+in).本文用初等方法给出了与有关的几个恒等式和不等式,并给出了一个对称不等式的初等证明.

Let n∈N°,r∈N,a1,a2,…,an∈C,and set En｜r｜=En[r]（a1,a2…,an）=∑i1＋i2＋…＋in=r a1^i1a2^i2…an^in where the sum goes through all the non - negative integral group （i1,i2,…,in）,satisfying i1＋i2＋…＋in=r In this paper, we use the elementary method to give several identities and inequalities related to En[r] , as well as the elementary proof of a symmetric inequality. I . .