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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 Generalized Appell polynomials ： ウィキペディア英語版 Generalized Appell polynomials In mathematics, a polynomial sequence $\backslash$ has a generalized Appell representation if the generating function for the polynomials takes on a certain form: :$K(z,w)\; =\; A(w)\backslash Psi(zg(w))\; =\; \backslash sum\_^\backslash infty\; p\_n(z)\; w^n$ where the generating function or kernel $K(z,w)$ is composed of the series :$A(w)=\; \backslash sum\_^\backslash infty\; a\_n\; w^n\; \backslash quad$ with $a\_0\; \backslash ne\; 0$ and :$\backslash Psi(t)=\; \backslash sum\_^\backslash infty\; \backslash Psi\_n\; t^n\; \backslash quad$ and all $\backslash Psi\_n\; \backslash ne\; 0$ and :$g(w)=\; \backslash sum\_^\backslash infty\; g\_n\; w^n\; \backslash quad$ with $g\_1\; \backslash ne\; 0.$ Given the above, it is not hard to show that $p\_n(z)$ is a polynomial of degree $n$. Boas–Buck polynomials are a slightly more general class of polynomials. ==Special cases== * The choice of $g(w)=w$ gives the class of Brenke polynomials. * The choice of $\backslash Psi(t)=e^t$ results in the Sheffer sequence of polynomials, which include the general difference polynomials, such as the Newton polynomials. * The combined choice of $g(w)=w$ and $\backslash Psi(t)=e^t$ gives the Appell sequence of polynomials. 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「Generalized Appell 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.