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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 Legendre rational functions ： ウィキペディア英語版 Legendre rational functions In mathematics the Legendre rational functions are a sequence of functions which are both rational and orthogonal. A rational Legendre function of degree ''n'' is defined as: :$R\_n(x)\; =\; \backslash frac\backslash ,L\_n\backslash left(\backslash frac\backslash right)$ where $L\_n(x)$ is a Legendre polynomial. These functions are eigenfunctions of the singular Sturm-Liouville problem: :$(x+1)\backslash partial\_x(x\backslash partial\_x((x+1)v(x)))+\backslash lambda\; v(x)=0$ with eigenvalues :$\backslash lambda\_n=n(n+1)\backslash ,$ == Properties== Many properties can be derived from the properties of the Legendre polynomials of the first kind. Other properties are unique to the functions themselves. 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「Legendre rational functions」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.