含幂函数、有理分式与三角函数的无穷积分——一个引理及其应用  

Infinite integrals involving powers,rational functions and trigonometric functions——a lemma and its application

作　　者：林琼桂[1] 

机构地区：[1]中山大学物理科学与工程技术学院,广东广州510275

出　　处：《大学物理》2015年第5期1-4,18,共5页College Physics

基　　金：国家自然科学基金项目(11175268)资助

摘　　要：介绍了新近建立的一个引理.该引理给出幂函数与指数函数之积沿大圆弧的积分.利用该引理和留数定理导出了含幂函数、有理分式与三角函数的无穷积分的一般公式,结果用留数和有理分式的洛朗系数表出.计算了若干实例.An introduction to a recently established lemma is presented. The lemma enables us to evaluate integrals involving powers and exponentials on a large semicircle. Based on the lemma and the residue theorem, two general for- mulae are derived for infinite integrals are expressed in terms of residues and involving powers, rational functions and trigonometric functions, and the results Laurent coefficients of the rational function. Several examples are given.

关 键 词：无穷积分 留数定理 幂函数 有理分式 三角函数 

分 类 号：O411.1[理学—理论物理]