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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 Dickman–de Bruijn function ： ウィキペディア英語版 Dickman function In analytic number theory, the Dickman function or Dickman–de Bruijn function ρ is a special function used to estimate the proportion of smooth numbers up to a given bound. It was first studied by actuary Karl Dickman, who defined it in his only mathematical publication, and later studied by the Dutch mathematician Nicolaas Govert de Bruijn. ==Definition== The Dickman-de Bruijn function $\backslash rho(u)$ is a continuous function that satisfies the delay differential equation :$u\backslash rho\text{'}(u)\; +\; \backslash rho(u-1)\; =\; 0\backslash ,$ with initial conditions $\backslash rho(u)\; =\; 1$ for 0 ≤ ''u'' ≤ 1. Dickman proved that, when $a$ is fixed, we have :$\backslash Psi(x,\; x^)\backslash sim\; x\backslash rho(a)\backslash ,$ where $\backslash Psi(x,y)$ is the number of ''y''-smooth (or ''y''-friable) integers below ''x''. Ramaswami later gave a rigorous proof that for fixed ''a'', $\backslash Psi(x,x^)$ was asymptotic to $x\; \backslash rho(a)$, with the error bound :$\backslash Psi(x,x^)=x\backslash rho(a)+O(x/\backslash log\; x)$ in big O notation. 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「Dickman 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.