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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 Trinomial expansion ： ウィキペディア英語版 Trinomial expansion In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by :$(a+b+c)^n\; =\; \backslash sum\_\}\; \backslash ,\; a^i\; \backslash ,\; b^\; \backslash ;\backslash !\; c^k,$ where is a nonnegative integer and the sum is taken over all combinations of nonnegative indices and such that .〔.〕 The trinomial coefficients are given by :$=\; \backslash frac\; \backslash ,.$ This formula is a special case of the multinomial formula for . The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.〔.〕 The number of terms of an expanded trinomial is the triangular number :$t\_\; =\; \backslash frac,$ where is the exponent to which the trinomial is raised.〔.〕 ==See also== * Binomial expansion * Pascal's pyramid * Multinomial coefficient * Trinomial triangle 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「Trinomial expansion」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.