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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 Buchstab function ： ウィキペディア英語版 Buchstab function The Buchstab function (or Buchstab's function) is the unique continuous function $\backslash omega:\; \backslash R\_\backslash rightarrow\; \backslash R\_$ defined by the delay differential equation :$\backslash omega(u)=\backslash frac\; 1\; u,\; \backslash qquad\backslash qquad\backslash qquad\; 1\backslash le\; u\backslash le\; 2,$ :$\}\; (u\backslash omega(u))=\backslash omega(u-1),\; \backslash qquad\; u\backslash ge\; 2.$ In the second equation, the derivative at ''u'' = 2 should be taken as ''u'' approaches 2 from the right. It is named after Alexander Buchstab, who wrote about it in 1937. ==Asymptotics== The Buchstab function approaches $e^$ rapidly as $u\backslash to\backslash infty,$ where $\backslash gamma$ is the Euler–Mascheroni constant. In fact, :$|\backslash omega(u)-e^|\backslash le\; \backslash frac,\; \backslash qquad\; u\backslash ge\; 1,$ where ''ρ'' is the Dickman function.〔(5.13), Jurkat and Richert 1965. In this paper the argument of ''ρ'' has been shifted by 1 from the usual definition.〕 Also, $\backslash omega(u)-e^$ oscillates in a regular way, alternating between extrema and zeroes; the extrema alternate between positive maxima and negative minima. The interval between consecutive extrema approaches 1 as ''u'' approaches infinity, as does the interval between consecutive zeroes.〔p. 131, Cheer and Goldston 1990.〕 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「Buchstab function」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.