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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 Stirling polynomials ： ウィキペディア英語版 Stirling polynomials In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, the Stirling numbers and the Bernoulli numbers. ==Definition and examples== For nonnegative integers ''k'', the Stirling polynomials ''S''''k''(''x'') are defined by the generating function equation ::$\backslash left(\; \backslash right)\; ^=\; \backslash sum\_^\backslash infty\; S\_k(x).$ The first 10 Stirling polynomials are: }(x+1)\, |- | align="center" | 2 | $\}\; (3x^2+5x+2)\; \backslash ,$ |- | align="center" | 3 | $\}\; (x^3+2x^2+x)\; \backslash ,$ |- | align="center" | 4 | $\}\; (15x^4+30x^3+5x^2-18x-8)\; \backslash ,$ |- | align="center" | 5 | $\}\; (3x^5+5x^4-5x^3-13x^2-6x)\; \backslash ,$ |- | align="center" | 6 | $\}\; (63x^6+63x^5-315x^4-539x^3-84x^2+236x+96)\; \backslash ,$ |- | align="center" | 7 | $\}\; (9x^7-84x^5-98x^4+91x^3+194x^2+80x)\; \backslash ,$ |- | align="center" | 8 | $\}\; (135x^8-180x^7-1890x^6-840x^5+6055x^4+8140x^3+884x^2-3088x-1152)\; \backslash ,$ |- | align="center" | 9 | $\}\; (15x^9-45x^8-270x^7+182x^6+1687x^5+1395x^4-1576x^3-2684x^2-1008x)\; \backslash ,$ |} 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「Stirling 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.