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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 Exponential formula ： ウィキペディア英語版 Exponential formula In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures. The exponential formula is a power-series version of a special case of Faà di Bruno's formula. ==Statement== For any formal power series of the form :$f(x)=a\_1\; x+x^2+x^3+\backslash cdots+x^n+\backslash cdots\backslash ,$ we have :$\backslash exp\; f(x)=e^=\backslash sum\_^\backslash infty\; x^n,\backslash ,$ where :$b\_n=\backslash sum\_\backslash cdots\; a\_,$ and the index π runs through the list of all partitions of the set . (When ''k'' = 0, the product is empty and by definition equals 1.) One can write the formula in the following form: :$b\_n\; =\; B\_n(a\_1,a\_2,\backslash dots,a\_n),$ and thus :$\backslash exp\backslash left(\backslash sum\_^\backslash infty\; x^n\; \backslash right)\; =\; \backslash sum\_^\backslash infty\; x^n,$ where ''B''''n''(''a''1, ..., ''a''''n'') is the ''n''th complete Bell polynomial. 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「Exponential formula」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.