Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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] Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, Second edition, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
  • [2] J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • [3] Rolf Nevanlinna and V. Paatero, Einführung in die Funktionentheorie, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, Mathematische Reihe, Band 30, Birkhäuser Verlag, Basel-Stuttgart, 1965 (German). MR 0201609

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Additional Information

DOI: http://dx.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