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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 Appell sequence ： ウィキペディア英語版 Appell sequence In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence ''n'' = 0, 1, 2, ... satisfying the identity :$p\_n(x)\; =\; np\_(x),$ and in which ''p''0(''x'') is a non-zero constant. Among the most notable Appell sequences besides the trivial example are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every Appell sequence is a Sheffer sequence, but most Sheffer sequences are not Appell sequences. ==Equivalent characterizations of Appell sequences== The following conditions on polynomial sequences can easily be seen to be equivalent: * For ''n'' = 1, 2, 3, ..., ::$p\_n(x)\; =\; np\_(x)$ :and ''p''0(''x'') is a non-zero constant; * For some sequence ''n'' = 0, 1, 2, ... of scalars with ''c''0 ≠ 0, ::$p\_n(x)\; =\; \backslash sum\_^n\; c\_k\; x^;$ * For the same sequence of scalars, ::$p\_n(x)\; =\; \backslash left(\backslash sum\_^\backslash infty\; D^k\backslash right)\; x^n,$ :where ::$D\; =\; ;$ * For ''n'' = 0, 1, 2, ..., ::$p\_n(x+y)\; =\; \backslash sum\_^n\; p\_k(x)\; y^.$ 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「Appell sequence」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.