一类含参级数的研究

A Study of Parametric Progression

本文以Euler极限为基础,引进一个新概念、含参变量级数,并推证了含参级数的若干性质和定理,证明了任何实数都可用含参级数表示,所列举的(3,5)、(3,6)式这一类求和问题,要用现有数学分析专著中的概念和方法是很难下手的。引入含参级数之后,为解决这一类问题,提供新的途径和方法。

Based on Euler's limit, a new idea of parametric progression is introduced, and I have proved a few properties and theorems of parametric progression in this paper. I also have given such examples as (3.1.5) (3.1.6) and about how to calculate their sum, this can not be found in Mathematical Analysis. (This is not talked about in Mathematical Analysis.) In fact, it is very difficult to deal with such problems by the already existing analytical concept and methods. After the parametric profrcssion is introduced, it provids us with a new simple way to deal with this kind of problem.