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Numerik: Implementierung Von Zylinderfunktionen by Johann-Jost Achenbach

Numerik: Implementierung Von Zylinderfunktionen

by Johann-Jost Achenbach
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Book cover type: Paperback
  • ISBN13: 9783528044626
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 236
  • Original Price: EUR 51.39
  • Language: German
  • Edition: 1986
  • Item Weight: 400 grams
  • BISAC Subject(s): Engineering (General)

Eine Klasse der hypergeometrischen Funktionen bilden die Zylinderfunktio- nen, die durch eine nach F. W. Bessel (1784 - 1846) benannte Differential- gleichung 2. Ordnung definiert und daher auch als Besselfunktionen bezeichnet werden. Die hypergeometrische Funktion ist durch die unendliche Potenzreihe o CI. - 13 _Cl._(, -Cl._+ 1-t.)_0 -: -13 0....., (_13+-: -1--'-.) 1 2 F(CI., S, y;x) + - 0 x + o x + .-... loy 1020yo(y+1) definiert, aus der sich viele spezielle Funktionen ableiten lassen, u.a. auch die Losung der o.g. Differentialgleichung. Zylinderfunktionen sind in der allgemeinen Physik haufig gebrauchte Funk- tionen, die sich analytisch durch.lntegralausdrUcke darstellen lassen und die Eigenschaft haben, daB sich relativ allgemein vorgebbare Funktionen in eine nach ihnen fortschreitende Reihe entwickeln lassen. Nachfolgend seien einige wichtige Gebiete genannt, in denen Zylinderfunk- tionen auftreten: Wellenausbreitung in Mechanik, Elektrodynamik, Optik und Wellen- mechanik (Quantentheorie); - Potentialtheorie; - Theorie schwingender Membranen und elastischer Korper; interferometrische Auswertung; Einleitung 2 - Astronomie; - Randwertaufgaben der Akustik und der Warmeleitung; - Hertzscher Dipol; Antennenprobleme; - Lichtleitung in Lichtwellenleitern; - Beugungsphanomene an Zylindern und Offnungen; - Behandlung der radialen Eigenfunktion wellenmechanischer Lasungen; - Entwicklungen nach Besselfunktionen (z.B. zur Darstellung des Amplitudenspektrums frequenzmodulierter Schwingungen); - Verbesserung des Obertragungsverhaltens digitaler Filter. Grundsatzlich kannen Zylinderfunktionen nach Art und Ordnung unterschie- den werden. Somit wird beispielsweise die Zylinderfunktion 1. Art und v- ter Ordnung als "einfache Besselfunktion v-ter Ordnung" benannt und mit Jv(z) bezeichnet.

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