| 二维无界连通域上反常积分敛散性的判别准则 |
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| 引用本文： | 廉海荣,魏亚欣,房世超,徐勐戬,闫小军.二维无界连通域上反常积分敛散性的判别准则[J].大学数学,2017,33(3):89-94. |
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| 作者姓名： | 廉海荣 魏亚欣 房世超 徐勐戬 闫小军 |
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| 作者单位： | 1. 中国地质大学(北京)数理学院,北京,100083;2. 北京师范大学数学科学学院,北京,100083;3. 北京交通大学电子信息工程学院,北京,100044 |
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| 基金项目： | 中央高校基本科研业务费专项资金资助 |
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| 摘 要： | 讨论了二维无界连通域上反常积分的敛散性.从柯西积分判别法出发,考察了三类特定区域上二元函数的反常积分,利用列维定理,得到了一些新的判别准则.
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| 关 键 词： | 二元函数反常积分 无界域 敛散性 绝对收敛 |
Criterion for Convergence of Improper Integrals on Two-dimensionUnbounded Connected Domains |
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| LIAN Hai-rong,WEI Ya-xin,FANG Shi-chao,XU Meng-jian,YAN Xiao-jun.Criterion for Convergence of Improper Integrals on Two-dimensionUnbounded Connected Domains[J].College Mathematics,2017,33(3):89-94. |
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| Authors: | LIAN Hai-rong WEI Ya-xin FANG Shi-chao XU Meng-jian YAN Xiao-jun |
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| Abstract: | Discusses the convergence and divergence of improper integrals for multi-variable function on the unbounded connected domains.By using the Cauchy integration criterion, we investigate the improper integral on three special domain.With the help of the Cauchy integration criterion and Levi theorem, new criteria for convergence and divergence are presented. |
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| Keywords: | improper integral of multi-variable function unbounded domain convergence and divergence absolute convergence |
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