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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 Natural logarithm of 2 ： ウィキペディア英語版 Natural logarithm of 2 The decimal value of the natural logarithm of 2 is approximately :$\backslash ln\; 2\; \backslash approx\; 0.69314718056$ as shown in the first line of the table below. The logarithm in other bases is obtained with the formula :$\backslash log\_b\; 2\; =\; \backslash frac.$ The common logarithm in particular is () :$\backslash log\_\; 2\; \backslash approx\; 0.301029995663981195.$ The inverse of this number is the binary logarithm of 10: :$\backslash log\_2\; 10=1/\backslash log\_\; 2\; \backslash approx\; 3.321928095$ (). ==Series representations== :$\backslash sum\_^\backslash infty\; \backslash frac\; =\; \backslash sum\_^\backslash infty\; \backslash frac\; =\; \backslash ln\; 2.$ :$\backslash sum\_^\backslash infty\; \backslash frac\; =\; 2\backslash ln\; 2\; -1.$ :$\backslash sum\_^\backslash infty\; \backslash frac\; =\; 2\backslash ln\; 2\; -1.$ :$\backslash sum\_^\backslash infty\; \backslash frac\; =\; \backslash ln\; 2\; -1.$ :$\backslash sum\_^\backslash infty\; \backslash frac\; =\; 2\backslash ln\; 2\; -\backslash frac.$ :$\backslash sum\_^\backslash infty\; \backslash frac()\; =\; \backslash ln\; 2\; -\backslash frac.$ :$\backslash sum\_^\backslash infty\; \backslash frac()\; =\; 1-\backslash gamma-\backslash frac\backslash ln\; 2.$ :$\backslash sum\_^\backslash infty\; \backslash frac\backslash zeta(2n)\; =\; \backslash frac(1-\backslash ln\; 2).$ :$\backslash ln\; 2\; =\; \backslash sum\_\; \backslash frac.$ :$\backslash ln\; 2\; =\; \backslash sum\_\backslash left(\backslash frac+\backslash frac\backslash right)\backslash frac.$ :$\backslash ln\; 2\; =\; \backslash frac\; +\; \backslash frac12\; \backslash sum\_\backslash left(\backslash frac+\backslash frac+\backslash frac+\backslash frac\backslash right)\backslash frac.$ :$\backslash ln\; 2\; =\; \backslash frac\; \backslash sum\_\; \backslash frac.$ :$\backslash ln\; 2\; =\; \backslash sum\_\; \backslash left(\; \backslash frac\{(2k+1)\; 49^\{2k+1\}\}\; \backslash right)\; .$ ($\backslash gamma$ is the Euler–Mascheroni constant and $\backslash zeta$ Riemann's zeta function). Some Bailey–Borwein–Plouffe (BBP)-type representations fall also into this category. 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「Natural logarithm of 2」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.