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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 Mashreghi–Ransford inequality ： ウィキペディア英語版 Mashreghi–Ransford inequality In Mathematics, the Mashreghi–Ransford inequality is a bound on the growth rate of certain sequences. It is named after J. Mashreghi and T. Ransford. Let $(a\_n)\_$ be a sequence of complex numbers, and let : $b\_n\; =\; \backslash sum\_^n\; a\_k,\; \backslash qquad\; (n\; \backslash geq\; 0),$ and : $c\_n\; =\; \backslash sum\_^n\; (-1)^\; a\_k,\; \backslash qquad\; (n\; \backslash geq\; 0).$ We remind that the binomial coefficients are defined by : $=\; \backslash frac.$ Assume that, for some $\backslash beta>1$, we have $b\_n\; =\; O(\backslash beta^n)$ and $c\_n\; =\; O(\backslash beta^n)$ as $n\; \backslash to\; \backslash infty$. Then : $a\_n\; =\; O(\backslash alpha^n)$, as $n\; \backslash to\; \backslash infty$, where $\backslash alpha=\backslash sqrt.$ Moreover, there is a universal constant $\backslash kappa$ such that :$\backslash left(\; \backslash limsup\_\; \backslash frac\; \backslash right)\; \backslash leq\; \backslash kappa\; \backslash ,\; \backslash left(\; \backslash limsup\_\; \backslash frac\; \backslash right)^\}\; \backslash left(\; \backslash limsup\_\; \backslash frac\; \backslash right)^\}.$ The precise value of $\backslash kappa$ is unknown. However, it is known that : $\backslash frac\{\backslash sqrt\{3\}\}\backslash leq\; \backslash kappa\; \backslash leq\; 2.$ ==References== * . 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「Mashreghi–Ransford inequality」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.