About: Residue theorem

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The theorem that complex contour integrals are simply the sums of residues of singularities contained within the contour

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  • matematikai állítás (hu)
  • mathematischer Satz (de)
  • théorème d'analyse complexe (fr)
  • twierdzenie analizy zespolonej dostarczające metody obliczania wartości całek krzywoliniowych (pl)
  • the theorem that complex contour integrals are simply the sums of residues of singularities contained within the contour (en)
  • el teorema que les integrals de contorn complexes són simplement les sumes de residus de singularitats contingudes dins del contorn (ca)
  • funktioteoriassa tulos, jonka avulla voidaan määrittää annetun funktion määrättyjä integraaleja (fi)
  • مبرهنة في التحليل المركب (ar)
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  • p/c020900 (en)
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  • Pick an arbitrary . As above, define By the Cauchy residue theorem, for all large enough such that encircles , It remains to prove the integral converges to zero. Since is an even function, and is symmetric about the origin, we have , and so (en)
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  • Proof (en)
  • Cauchy integral theorem (en)
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  • Residue theorem (en)
  • Teorema de los residuos (es)
  • Théorème des résidus (fr)
  • Residuensatz (de)
  • Teorema dei residui (it)
  • Residustelling (nl)
  • Teorema dos resíduos (pt)
  • Twierdzenie o residuach (pl)
  • Основная теорема о вычетах (ru)
  • Residysatsen (sv)
  • Основна теорема про лишки (uk)
  • 留数定理 (zh)
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