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A brief proof of Cauchy's integral theorem


Author: John D. Dixon
Journal: Proc. Amer. Math. Soc. 29 (1971), 625-626
MSC: Primary 30.35
DOI: https://doi.org/10.1090/S0002-9939-1971-0277699-8
MathSciNet review: 0277699
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Abstract: A short proof of Cauchy's theorem for circuits homologous to 0 is presented. The proof uses elementary local properties of analytic functions but no additional geometric or topological arguments.


References [Enhancements On Off] (What's this?)

  • [1] L. V. Ahlfors, Complex analysis: An introduction to the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill, New York, 1966. MR 32 #5844. MR 0188405 (32:5844)
  • [2] J. Dieudonné, Foundations of modern analysis, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074. MR 0120319 (22:11074)
  • [3] R. Nevanlinna and V. Paatero, Einführung in die Funktionentheorie, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, Mathematische Reihe, Band 30, Birkhäuser Verlag, Basel, 1965; English transl., Addison-Wesley, Reading, Mass., 1969. MR 34 #1491; MR 39 #415. MR 0201609 (34:1491)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0277699-8
Keywords: Cauchy's integral theorem, Cauchy's integral formula, residue theorem
Article copyright: © Copyright 1971 American Mathematical Society

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