Excerpt from Theorie der Doppeltperiodischen Functionen Einer Ver???nderlichen Gr???sse, Vol. 2 Der zweite Band meines Werkes ???ber doppeltperiodische F unc tionen, welcher hiermit der Oeffentlichkeit ???bergeben wird, zerf???llt in drei Theile, von denen der erste die Anf???nge der Transformations theorie auf der Grundlage von Additionstheoremen zwischen Theta functionen mit verschiedenen Moduln, der zweite die Entwickelung der doppeltperiodischen Functionen, insbesondere zweiter und dritter Art, in trigonometrische ...
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Excerpt from Theorie der Doppeltperiodischen Functionen Einer Ver???nderlichen Gr???sse, Vol. 2 Der zweite Band meines Werkes ???ber doppeltperiodische F unc tionen, welcher hiermit der Oeffentlichkeit ???bergeben wird, zerf???llt in drei Theile, von denen der erste die Anf???nge der Transformations theorie auf der Grundlage von Additionstheoremen zwischen Theta functionen mit verschiedenen Moduln, der zweite die Entwickelung der doppeltperiodischen Functionen, insbesondere zweiter und dritter Art, in trigonometrische Reihen, der dritte endlich die mannigfaltigen Difl'erentialgleichungen behandelt, denen die Functionen zweiter Art Gen???ge leisten. Diese Theorien sind wohl bisher in keinem Werk vereinigt worden. Urspr???nglich war es meine Absicht, dieselben allein mit denjenigen zu ver???ffentlichen, die sich im vierten Abschnitt und einigen Paragraphen der vorangehenden Abschnitte des ersten Bandes befinden. Durch die Natur des behandelten Gegenstandes sah ich mich aber veranlasst, von meinem urspr???nglichen Plane abzugehen und die schon vielfach behandelten elliptischen Functionen mit in den Kreis der Betrachtungen hineinzuziehen. Der Zusammenhang zwischen den gew???hnlichen elliptischen Functionen und den Functionen zweiter und dritter Art ist n???mlich ein so enger, dass die gesonderte Betrachtung der letzteren eines nat???rlichen Rahmens, sowie eines einheitlichen Ge sicht3punktes entbehren w???rde und zu mannigfachen Uebelst???nden ge fiihrt h???tte. Wie ich aber schon in der Vorrede zum ersten Bande bemerkt habe und nochmals ausdr???cklich hervorheben m???chte, ist es keineswegs meine Absicht gewesen, eine alles umfassende Theorie der elliptischen Functionen zu geben. Es sind im Wesentlichen nur diejenigen allgemeinen und bekannten Untersuchungen hineingezogen worden, welche die Grundlage und die Gesichtspunkte f???r das ganze Werk abgeben und zum Verst???ndniss der Theorie der Functionen zweiter und dritter Art nothwendig sind diese letzteren bilden den eigentlichen Schwerpunkt meines Werkes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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