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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 Stolarsky mean ： ウィキペディア英語版 Stolarsky mean In mathematics, the Stolarsky mean of two positive real numbers ''x'', ''y'' is defined as: :$$ \begin S_p(x,y) & = \lim_ \left(}\right)^ \\() & = \begin x & \textx=y \\ \left(}\right)^ & \text \end \end It is derived from the mean value theorem, which states that a secant line, cutting the graph of a differentiable function $f$ at $(\; x,\; f(x)\; )$ and $(\; y,\; f(y)\; )$, has the same slope as a line tangent to the graph at some point $\backslash xi$ in the interval $()$. :$\backslash exists\; \backslash xi\backslash in()\backslash \; f\text{'}(\backslash xi)\; =\; \backslash frac$ The Stolarsky mean is obtained by :$\backslash xi\; =\; f\text{'}^\backslash left(\backslash frac\backslash right)$ when choosing $f(x)\; =\; x^p$. == Special cases == *$\backslash lim\_\; S\_p(x,y)$ is the minimum. *$S\_(x,y)$ is the geometric mean. *$\backslash lim\_\; S\_p(x,y)$ is the logarithmic mean. It can be obtained from the mean value theorem by choosing $f(x)\; =\; \backslash ln\; x$. *$S\_\}(x,y)$ is the power mean with exponent $\backslash frac$. *$\backslash lim\_\; S\_p(x,y)$ is the identric mean. It can be obtained from the mean value theorem by choosing $f(x)\; =\; x\backslash cdot\; \backslash ln\; x$. *$S\_2(x,y)$ is the arithmetic mean. *$S\_3(x,y)\; =\; QM(x,y,GM(x,y))$ is a connection to the quadratic mean and the geometric mean. *$\backslash lim\_\; S\_p(x,y)$ is the maximum. 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「Stolarsky mean」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.