翻訳と辞書 Words near each other ・ Merton Park Ward Residents Association ・ Merton Passage ・ Merton Priory ・ Merton Professors ・ Merten (name) ・ Merten de Keyser ・ Merten Mauritz ・ Merten station ・ Mertendorf ・ Mertendorf, Thuringia ・ Mertens ・ Mertens conjecture ・ Mertens function ・ Mertens v. Hewitt Associates ・ Mertens' theorem ・ Mertens' theorems ・ Mertens' water monitor ・ Mertens, Texas ・ Mertens-stable equilibrium ・ Mertensi ・ Mertensia ・ Mertensia bella ・ Mertensia ciliata ・ Mertensia longiflora ・ Mertensia maritima ・ Mertensia oblongifolia ・ Mertensia ovum ・ Mertensia paniculata ・ Mertensia virginica ・ Mertensii Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mertens' theorems ： ウィキペディア英語版 Mertens' theorems In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.〔F. Mertens. J. reine angew. Math. 78 (1874), 46-62 (Ein Beitrag zur analytischen Zahlentheorie )〕 "Mertens' theorem" may also refer to his theorem in analysis. == In number theory == In the following, let $p\backslash le\; n$ mean all primes not exceeding ''n''. Mertens' 1st theorem: :$\backslash sum\_\; \backslash frac\; -\; \backslash ln\; n$ does not exceed 2 in absolute value for any $n\backslash ge\; 2$. Mertens' 2nd theorem: :$\backslash lim\_\backslash left(\backslash sum\_\backslash frac1p\; -\backslash ln\backslash ln\; n-M\backslash right)\; =0,$ where ''M'' is the Meissel–Mertens constant. More precisely, Mertens〔 proves that the expression under the limit does not in absolute value exceed :$\backslash frac\; 4\; +\backslash frac\; 2$ for any $n\backslash ge\; 2$. Mertens' 3rd theorem: :$\backslash lim\_\backslash ln\; n\backslash prod\_\backslash left(1-\backslash frac1p\backslash right)=e^,$ where γ is the Euler–Mascheroni constant. 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「Mertens' theorems」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.