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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 Krawtchouk polynomials ： ウィキペディア英語版 Kravchuk polynomials Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian name "Кравчу́к") are discrete orthogonal polynomials associated with the binomial distribution, introduced by . The first few polynomials are (for ''q''=2): * $\backslash mathcal\_0(x;\; n)\; =\; 1$ * $\backslash mathcal\_1(x;\; n)\; =\; -2x\; +\; n$ * $\backslash mathcal\_2(x;\; n)\; =\; 2x^2\; -\; 2nx\; +$ * $\backslash mathcal\_3(x;\; n)\; =\; -\backslash fracx^3\; +\; 2nx^2\; -\; (n^2\; -\; n\; +\; \backslash frac)x\; +\; .$ The Kravchuk polynomials are a special case of the Meixner polynomials of the first kind. ==Definition== For any prime power ''q'' and positive integer ''n'', define the Kravchuk polynomial :$\backslash mathcal\_k(x;\; n)\; =\; \backslash mathcal\_k(x)\; =\; \backslash sum\_^(-1)^j\; (q-1)^\; \backslash binom\; \backslash binom,\; \backslash quad\; k=0,1,\; \backslash ldots,\; n.$ 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「Kravchuk 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.