存在可去型奇点包含正余弦函数的无穷积分的新算法  

THE NEW ALGORITHMS FOR THE INFINITE INTEGRATION OF THE FUNCTIONS WHO HAVE REMOVABLE SINGULAR POINTS AND CONTAIN SINE AND COSINE FUNCTIONS

作　　者：文军 冯丹丹 杨阳 文政 WEN Jun;FENG Dandan;YANG Yang;WEN Zheng(School of Mathematics,Physics and Statistics,Sichuan Minzu college,Ganzi Sichuan 626001;Department of Basic Courses,Army Academy of Border and Coastal Defence,Xi'an,Shaanxi 710108)

机构地区：[1]四川民族学院数理与统计学院,四川甘孜626001 [2]陆军边海防学院基础部,陕西西安710108

出　　处：《物理与工程》2024年第5期23-26,33,共5页Physics and Engineering

基　　金：四川民族学院自办科研项目(考虑退激发能情况下超新星爆炸所需56-Ni质量的估算,XYZB2310ZB)。

摘　　要：受到《数学物理方法》教材上计算含有三角函数无穷积分计算公式的启发,本文主要讨论该类积分的被积函数在实轴上存在可去型奇点的情况。尽管这类问题可以使用围道积分方法完成,但比较烦琐,因此我们对这类问题的被积分函数进行处理,从形式上使被积分函数实轴上的奇点消失,使用教材上的公式先完成积分,再根据特定情况下极限与积分计算顺序可交换理论得到被积函数存在可去型奇点这类积分的值。理论与实际示例证明了我们方法的正确性。Inspired by the calculation formulas for infinite integrals containing trigonometric functions in the textbook“Mathematical Physics Methods”,this paper mainly discusses the case where the integrand of such integrals has removable singularities on the real axis.Although this kind of problems can be solved using the integral contour,the method is quite complicated.Therefore,we replace the function integrated by another one which has no singular points on the real axis formally,and we use the formulas which results from the textbook to solve the integration whose function integrated has no singular points on the real axis formally,and then,according to the theory that the order can be exchanged for the integration and limitation under the certain conditions,we can obtain the results of the integration whose function integrated has removable singular points.Finally,the correctness of our method is proven through theoretical and practical examples.

关 键 词：留数 围道积分 三角函数 奇点 

分 类 号：G642[文化科学—高等教育学] O411.1-4[文化科学—教育学]