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Proceedings of the American Mathematical Society

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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
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?)

  • Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
  • J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • 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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Keywords: Cauchy’s integral theorem, Cauchy’s integral formula, residue theorem
Article copyright: © Copyright 1971 American Mathematical Society