Cauchy integral formula
Cauchy-Goursat integral theorem is pivotal, fundamentally important, and well celebrated result in complex integral calculus. It requires analyticity of the function inside and on the boundary of the simple closed curve. In this study we will investigate the condition(s) under which integration of f...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2013
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| Online Access: | http://irep.iium.edu.my/36397/ http://irep.iium.edu.my/36397/1/1757-899X_53_1_012003.pdf |
| _version_ | 1848781222389481472 |
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| author | Azram, Mohammad Elfaki, Faiz Ahmed Mohamed |
| author_facet | Azram, Mohammad Elfaki, Faiz Ahmed Mohamed |
| author_sort | Azram, Mohammad |
| building | IIUM Repository |
| collection | Online Access |
| description | Cauchy-Goursat integral theorem is pivotal, fundamentally important, and well celebrated result in complex integral calculus. It requires analyticity of the function inside and on the boundary of the simple closed curve. In this study we will investigate the condition(s) under which integration of f(z) along the close contour C is equal to zero, even though the function is not analytic at a point inside C. Consequently,we will extend the above notion to a finite numbers of points and will present an easy and simple proof of unquestionably the most important, significant and pivotal result known as Cauchy integral formula. |
| first_indexed | 2025-11-14T15:46:08Z |
| format | Article |
| id | iium-36397 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:46:08Z |
| publishDate | 2013 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-363972014-04-25T07:45:23Z http://irep.iium.edu.my/36397/ Cauchy integral formula Azram, Mohammad Elfaki, Faiz Ahmed Mohamed QA Mathematics Cauchy-Goursat integral theorem is pivotal, fundamentally important, and well celebrated result in complex integral calculus. It requires analyticity of the function inside and on the boundary of the simple closed curve. In this study we will investigate the condition(s) under which integration of f(z) along the close contour C is equal to zero, even though the function is not analytic at a point inside C. Consequently,we will extend the above notion to a finite numbers of points and will present an easy and simple proof of unquestionably the most important, significant and pivotal result known as Cauchy integral formula. IOP Publishing 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/36397/1/1757-899X_53_1_012003.pdf Azram, Mohammad and Elfaki, Faiz Ahmed Mohamed (2013) Cauchy integral formula. IOP Conference Series: Materials Science and Engineering, 53. pp. 1-5. ISSN 1757-8981 http://iopscience.iop.org/1757-899X/53/1 doi:10.1088/1757-899X/53/1/012003 |
| spellingShingle | QA Mathematics Azram, Mohammad Elfaki, Faiz Ahmed Mohamed Cauchy integral formula |
| title | Cauchy integral formula |
| title_full | Cauchy integral formula |
| title_fullStr | Cauchy integral formula |
| title_full_unstemmed | Cauchy integral formula |
| title_short | Cauchy integral formula |
| title_sort | cauchy integral formula |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/36397/ http://irep.iium.edu.my/36397/ http://irep.iium.edu.my/36397/ http://irep.iium.edu.my/36397/1/1757-899X_53_1_012003.pdf |