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发散级數求和,现在还很难说是一个独立的数学分支,在数学中它主要是作为一个工具出现的。我们知道,级数的主要作用是表示函数,虽然它的每一项可以是极其簡單的函数(通常是初等函数),但所表示的函数却能够具有很复杂的性质,因而成为研究函数的一个不可缺少的工具。函数与表达它的级数的一种联系是通常意义的收敛,但这在级数发散(或还不知道它是否收敛)时就完全失去了作用。发散级数求和理论正是为了补充通常级数理论的这一点不足而建立起来的。本文的目的是在数学分析的基础上,向读者简单介绍这方面的一些基本概念、知议和一些最初等的有趣的应用。发散级数求和所涉及的方法,在古典分析中是比较典型的,因此一些主要定理的证明我们还是引出来。这里只要求读者具有一般分析的基础。
The sum of divergence progressions is hardly an independent branch of mathematics. In mathematics, it is mainly used as a tool. We know that the main function of the series is to represent the function. Although each of its functions can be an extremely simple function (usually an elementary function), the represented function can have a very complex nature and thus become a research function. Indispensable tools. A connection between a function and the series in which it is expressed is a convergence of the usual sense, but this completely loses its function when the series is divergence (or if it is not yet known whether it converges). The theory of divergence series summation was established to supplement this deficiency of the usual series theory. The purpose of this article is to provide readers with a brief introduction to basic concepts, knowledge, and some initial and other interesting applications based on mathematical analysis. The methods involved in the summation of divergence series are typical in classical analysis. Therefore, some of the major theorems are still derived. Here only the reader is required to have a basis for general analysis.