3个级数乘法定理辨析

Analysis on Theorems of Series Multiplication

由于级数乘法没有对乘积项的排列顺序加以定义,所以级数乘法的研究和内容比较复杂。涉及级数乘法的3个乘法定理(Cauchy定理、Mertens定理、Abel级数乘法定理)在形式和应用上既有相似之处也有很大区别。通过对3个乘法定理的条件的分析,着重指出了3个定理的不同之处,并通过例题对定理的应用技巧进行了说明。

The contents and studies on series multiplication are quite complicated because there is no definition on sequence of product items got by multiplication of series.There are obvious similarities and also differences in their expressions and applications among three theorems involving the series multiplication.In-depth analysis is made by discriminating the conditions of the theorems,and the differences are emphasized.The application techniques of theorems are demonstrated with examples.