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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 Secondary polynomials ： ウィキペディア英語版 Secondary polynomials In mathematics, the secondary polynomials $\backslash$ associated with a sequence $\backslash$ of polynomials orthogonal with respect to a density $\backslash rho(x)$ are defined by : $q\_n(x)\; =\; \backslash int\_\backslash mathbb\backslash !\; \backslash frac\; \backslash rho(t)\backslash ,dt.$ To see that the functions $q\_n(x)$ are indeed polynomials, consider the simple example of $p\_0(x)=x^3.$ Then, : & \rho(t)\,dt \\ & = \int_\mathbb \! t^2\rho(t)\,dt + x\int_\mathbb \! t\rho(t)\,dt + x^2\int_\mathbb \! \rho(t)\,dt \end which is a polynomial $x$ provided that the three integrals in $t$ (the moments of the density $\backslash rho$) are convergent. ==See also== * Secondary measure 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「Secondary polynomials」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.