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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Conical function ： ウィキペディア英語版 Conical function In mathematics, conical functions or Mehler functions are functions which can be expressed in terms of Legendre functions of the first and second kind, $P^\backslash mu\_(x)$ and $Q^\backslash mu\_(x).$ The functions $P^\backslash mu\_(x)$ were introduced by Gustav Ferdinand Mehler, in 1868, when expanding in series the distance of a point on the axis of a cone to a point located on the surface of the cone. Mehler used the notation $K^\backslash mu(x)$ to represent these functions. He obtained integral representation and series of functions representations for them. He also established an addition theorem for the conical functions. Carl Neumann obtained an expansion of the functions $K^\backslash mu(x)$ in terms of the Legendre polynomials in 1881. Leonhardt introduced for the conical functions the equivalent of the spherical harmonics in 1882. ==External links== * * G. F. Mehler "(Ueber die Vertheilung der statischen Elektricität in einem von zwei Kugelkalotten begrenzten Körper )" ''Journal für die reine und angewandte Mathematik'' 68, 134 (1868). * G. F. Mehler "(Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung )" ''Mathematische Annalen'' 18 p. 161 (1881). * C. Neumann "(Ueber die Mehler'schen Kegelfunctionen und deren Anwendung auf elektrostatische Probleme )" ''Mathematische Annalen'' 18 p. 195 (1881). * G. Leonhardt "( 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Conical function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.