幂平均数若干性质之证明

Proving of Several Properties of the k'th Sample Moment About Zero

幂平均数作为算术平均数、几何平均数、调和平均数等的一般形式,它与各具体形式之间必存在一定的关系。在目前的一些教材中,这种逻辑关系的描述是不正确的。又由于这些教材对所作的描述并未给予证明,因此,错误被隐藏起来。本文重新描述这种逻辑关系,并给予数学证明。

The k'th Sample Moment About Zero gives a general form for Mean, Geometric Mean , Harmonic Mean, and so forth. Thus, there are some logical relations existing between the properties of the general form and that of the various concrete forms. However, these logical relations are incorrectly narrated in some current textbooks. And further more, because they are not proved there yet, so the errors are hidden. This article narrates these relations once again, and gives mathematical proofs.