留数定理的推广及其应用

<正> 在留数定理中,总是假定函数在区域内孤立奇点的个数为有限个。本文引入了单值解析函数在其非孤立奇点处留数的概念,把留数定理推广到函数在区域内有无穷多个孤立奇点的情形,并应用这种推广极其简单地解决了某些级数的求和问题。

Generalization of the Residue Theorem and its Application

In this paper ,we introduced the concept of residue for a single-valued analytic function at its non-isolated singular points , and we extended the residue theorem to the case in which, a function has an infinite number of singlarities. As an application of the extended residue theorem we solved very simply the problem of summaton for certain series.