反常重积分与反常累次积分  

Anomalous Double Integral and Anomalous Iterated Integral

作　　者：张忠祥[1] ZHANG Zhong-xiang(School of Mathematics and Statistics, Wuhan University,Wuhan 430072, China)

机构地区：[1]武汉大学数学与统计学院

出　　处：《大学数学》2019年第3期103-110,共8页College Mathematics

基　　金：国家自然科学基金面上项目(11471250)

摘　　要：反常重积分的敛散性判别及其计算是数学分析中的一个难点,给出了类似于文献[1-2,7]中一个关于反常重积分收敛的充分性定理及完整证明,并在此基础上进行进一步推广,建立了反常重积分和反常累次积分的关系;另一方面,还从另一个角度给出了反常重积分和反常累次积分的关系.此外,给出了瑕重积分的相应定理.上述结论对于反常重积分的敛散性判别及其计算带来了极大的方便.The convergence, divergence and calculation of anomalous double integral are difficult in mathematical analysis. In this paper, we first prove an important theorem on convergence of anomalous double integral which is similar to the result in [1-2, 7], and then we generalize it to different cases. We built the relation between anomalous double integral and anomalous iterated integral. We also show the close relation between anomalous double integral and anomalous iterated integral from the other point of view. We give the corresponding results on weak singular double integral and weak singular iterated integral. The results in this paper are important and convenient for the convergence, divergence and calculation of anomalous double integral and anomalous iterated integral.

关 键 词：反常重积分 反常累次积分 敛散性 

分 类 号：O172.2[理学—数学]