| 关于多连域内Cauchy积分定理的两种新证法 |
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| 引用本文： | 傅孙瑜.关于多连域内Cauchy积分定理的两种新证法[J].天津理工大学学报,1988(2). |
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| 作者姓名： | 傅孙瑜 |
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| 作者单位： | 天津理工学院数理译丛编辑部 |
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| 摘 要： | 本文给出了多连域内Cauchy积分定理的两种新证法,一是以双连域内Cauchy积分定理为基础,并用数学归纳法加以证明;二是把问题转化为单连域的情形,并且应用单连城内的Cauchy积分定理,在此基础上,证明多连域内Cauchy积分定理,这两种新证法比通常的证法简明,推导颇为简捷,方法也易于掌握。
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| 关 键 词： | Cauchy积分定理 多连域 单连域 |
ON TWO KINDS OF NEW PROOF OF CAUCHY'S INTEGRAL THEOREM IN COMPLEX CONNECTED DOMAIN |
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| Fu Sunyu.ON TWO KINDS OF NEW PROOF OF CAUCHY''''S INTEGRAL THEOREM IN COMPLEX CONNECTED DOMAIN[J].Journal of Tianjin University of Technology,1988(2). |
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| Authors: | Fu Sunyu |
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| Abstract: | In this paper, two kinds of new proof of Cauchy's integral theorem in complex con- nected domain are given. The first one is based on the Cauchy's integral theorem in doubly connected domain, and proved with mathematical induction. The second one is turn the problem into the ease of a simply connected domain, and by using Cauchy's integral theo- rem in it. Based on this, we proved Cauchy's integral theorem in complex connected do- main. These two kinds of new proof are simpler than ordinary proof, and the process of derivation is simple, so new kinds of proof are easy to master. |
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| Keywords: | Cauchy's integral theorem Complex connected doman Simply connected domain |
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