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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 Rodrigues' formula ： ウィキペディア英語版 Rodrigues' formula In mathematics, Rodrigues's formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by , and . The name "Rodrigues formula" was introduced by Heine in 1878, after Hermite pointed out in 1865 that Rodrigues was the first to discover it. The term is also used to describe similar formulas for other orthogonal polynomials. describes the history of the Rodrigues formula in detail. ==Statement== Rodrigues stated his formula for Legendre polynomials $P\_n$: :$P\_n(x)\; =\; \backslash left((x^2\; -1)^n\; \backslash right).$ Laguerre polynomials are usually denoted ''L''0, ''L''1, ..., polynomial sequence and the Rodrigues formula can be written as, :$L\_n(x)=\backslash frac\backslash frac\backslash left(e^\; x^n\backslash right)\; =\backslash frac\; \backslash left(\; \backslash frac\; -1\; \backslash right)\; ^n\; x^n,$ The Rodrigues formula for the Hermite polynomial can be written as ::$H\_n(x)=(-1)^n\; e^\backslash frace^=\backslash left\; (2x-\backslash frac\; \backslash right\; )^n\; \backslash cdot\; 1$. Similar formule holds for many other sequences of orthogonal functions arising from Sturm-Liouville equations, and these are also called the Rodrigues formula for that case, especially when the resulting sequence is polynomial. 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「Rodrigues' formula」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.