再谈由留数定理求解的两类无穷积分  

Further discussion on two types of infinite integral treated by residue theorem

作　　者：周运清 黄文涛 ZHOU Yun-qing;HUANG Wen-tao(Department of physics,School of Information Engineering,Zhejiang Ocean University,Zhoushan Zhejian 316022,China)

机构地区：[1]浙江海洋大学信息工程学院物理系,浙江舟山316022

出　　处：《大学物理》2022年第9期24-27,42,共5页College Physics

基　　金：浙江省教育厅项目;浙江海洋大学课程思政项目资助。

摘　　要：受到文章[1]的启发,本文再次探讨由留数定理求解的两类无穷积分.首先分析两类积分的特征,并通过对文献[1]的方法进行梳理和简化,用留数定理对两类积分进行了处理,得到了n大于1且为整数情况下的结果,然后通过多值函数留数定理的方法对两类积分进行了重新计算,得到n大于1情况下的结果,并对结果进行了简要的说明.通过两种方法对积分的处理,体会留数定理的妙处,拓展学生的视野,提升学习的热情,为后续课程打好基础.Inspired by the article[1], this paper discusses two kinds of infinite integrals solved by residue theorem again. Firstly, some characteristics of the two kinds of integrals are analyzed concisely. By combing and simplifying the method in the article[1], the two kinds of integrals are processed with the residue theorem, and the results are obtained when they are greater than 1 and are integers. Then, the two kinds of integrals are recalculated by the method of the residue theorem of multivalued function, the results are obtained when they are greater than 1, and the results are briefly explained. Through the treatment of integral by two methods, we can experience the beauty of residue theorem, expand students’ vision and enhance their enthusiasm for learning, and lay a good foundation for their subsequent courses.

关 键 词：无穷积分 留数定理 多值函数 

分 类 号：O411.1[理学—理论物理]