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Über die Differentialgleichungen dritter Ordnung, welchen die Formen mit linearen Transformationen in sich genügen

In: Mathematische Werke

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  • Adolf Hurwitz

Abstract

Zusammenfassung Jacobi hat mit Hilfe von Formeln aus der Theorie der elliptischen Punktionen gezeigt, dass die Funktion ϑ s ( 0 ) = 1 + 2 q + 2 q 4 + 2 q 9 + ... $${\vartheta _s}(0) = 1 + 2q + 2{q^4} + 2{q^9} + ...$$ einer algebraischen Differentialgleichung dritter Ordnung genügt, von welcher zugleich ϑ 2(0) und ϑ 0(0) Lösungen sind1). In den folgenden Zeilen möchte ich nachweisen, dass diese Differentialgleichung nur ein Beispiel eines allgemeinen Satzes bildet, welcher der Theorie der Funktionen mit linearen Transformationen in sich angehört.

Suggested Citation

  • Adolf Hurwitz, 1932. "Über die Differentialgleichungen dritter Ordnung, welchen die Formen mit linearen Transformationen in sich genügen," Springer Books, in: Mathematische Werke, chapter 0, pages 287-294, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-4161-0_15
    DOI: 10.1007/978-3-0348-4161-0_15
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