几何-调和平均和一些平均值的特征(英文)

Geometric-Harmonic Mean and Characterizations of Some Mean-Values

中文关键词:  算术平均  几何平均  调和平均  几何-调和平均  第一类完全椭圆积分

英文关键词:Arithmetic mean  geometric mean  harmonic mean  geometric-harmonic mean  first complete elliptic integral.

中文摘要:

      本文的目的是直接证明任何两个正数的几何-调和平均值都可以用第一类完全椭圆积分来计算,并且给出一些平均值新的特征.

英文摘要:

      The purpose of this paper is to provide a direct proof on the fact that the geometric-harmonic mean of any two positive numbers can be calculated by a first complete elliptical integral, and then to give new characterizations of some mean-values.