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Unendliche Reihen

In: Höhere Mathematik griffbereit

Author

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  • M. J. Wygodski

Abstract

Zusammenfassung Zur Überwindung der Schwierigkeiten, die bei manchen Integrationen auftraten, drückten Newton und Leibniz den Integranden durch ein Polynom mit unendlich vielen Gliedern aus (s. § 270). Durch Anwendung der üblichen algebraischen Regeln auf derartige Ausdrücke machten die Mathematiker des 18. Jahrhunderts bemerkenswerte Entdeckungen. Jedoch zeigte es sich, daß man bei der vorbehaltslosen Anwendung der Regeln der Algebra auf unendliche Summen Irrtümer unterlaufen kann. Es ergab sich die Notwendigkeit, die Grundbegriffe exakt zu formulieren und Beweise für die Eigenschaften unendlicher Reihen zu konstruieren. Diese Aufgabe wurde von den Mathematikern im 19. Jahrhundert gelöst.

Suggested Citation

  • M. J. Wygodski, 1976. "Unendliche Reihen," Springer Books, in: Höhere Mathematik griffbereit, edition 2, chapter 0, pages 523-604, Springer.
    • Handle: RePEc:spr:sprchp:978-3-322-90113-2_7
    DOI: 10.1007/978-3-322-90113-2_7
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