Ueber Riemannís Theorie der Algebraischen Functionen

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Author: Felix Klein
Published: 2007
Language: German
Wordcount: 24,463 / 98 pg
Downloads: 1,681
Added to site: 2007.01.09
mnybks.net#: 15764
Genre: Non-fiction
Excerpt

von Kreisen, welche alle die feste Richtung [formula] berühren. Die Kreise sind um so kleiner, je grösser der absolute Betrag von Const. genommen wird. In ähnlicher Weise verlaufen daher die Curven [formula] Const. in der Nähe der Unstetigkeitsstelle. Insbesondere haben sie für sehr grosse positive oder negative Werthe von Const. die Gestalt kleiner, geschlossener, kreisähnlicher Ovale.--Für den imaginären Theil des Ausdrucks rechter Hand und also die Curven [formula] Const. gilt eine ähnliche Discussion. Der Unterschied ist nur der, dass jetzt die Richtung [formula] von allen Curven berührt wird. Hiernach wird die folgende Figur, in welcher die Niveaucurven wieder punctirt, die Strömungscurven ausgezogen sind, verständlich sein:

[Illustration: Figur 4.]

Figur 4.

Die analoge Discussion liefert vom [formula]-fachen algebraischen Unstetigkeitspuncte die erforderliche Anschauung. Ich will hier nur das Resultat anf

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