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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 Prouhet–Thue–Morse constant ： ウィキペディア英語版 Prouhet–Thue–Morse constant In mathematics, the Prouhet–Thue–Morse constant, named for Eugène Prouhet, Axel Thue, and Marston Morse, is the number—denoted by $\backslash tau$—whose binary expansion .01101001100101101001011001101001... is given by the Thue–Morse sequence. That is, : $\backslash tau\; =\; \backslash sum\_^\; \backslash frac^\; (-1)^\; \backslash ,\; x^i\; =\; \backslash frac\; -\; 2\; \backslash sum\_^\; t\_i\; \backslash ,\; x^i$ and can be expressed as : $\backslash tau(x)\; =\; \backslash prod\_^\; (\; 1\; -\; x^\; ).$ This is the product of Frobenius polynomials, and thus generalizes to arbitrary fields. The Prouhet–Thue–Morse constant was shown to be transcendental by Kurt Mahler in 1929. ==Notes== 〔 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「Prouhet–Thue–Morse constant」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.