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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 Half-exponential function ： ウィキペディア英語版 Half-exponential function In mathematics, a half-exponential function is a function ''ƒ'' so that if ''ƒ'' is composed with itself the result is exponential: : $f(f(x))\; =\; ab^x.\; \backslash ,$ Another definition is that ''ƒ'' is half-exponential if it is non-decreasing and ''ƒ''−1(''x''''C'') ≤ o(log ''x''). for every ''C'' > 0. It has been proven that every function ''ƒ'' composed of basic arithmetic operations, exponentials, and logarithms, then ''ƒ''(''ƒ''(''x'')) is either subexponential or superexponential: half-exponential functions are not expressible in terms of elementary functions. There are infinitely many functions whose self-composition is the same exponential function as each other. In particular, for every $A$ in the open interval $(0,1)$ and for every continuous strictly increasing function ''g'' from $()$ onto $()$, there is an extension of this function to a continuous monotonic function $f$ on the real numbers such that $f(f(x))=\backslash exp\; x$. In particular, :$f\; (x)\; =$ \begin g (x) & \mbox x \in (), \\ \exp (g^ (x)) & \mbox x \in (A,1], \\ \exp (f ( \ln (x))) & \mbox x \in (1,\infty), \\ \ln (f ( \exp (x))) & \mbox x \in (-\infty,0). \\ \end Half-exponential functions are used in computational complexity theory for growth rates "intermediate" between polynomial and exponential.〔 ==See also== * Functional square root 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「Half-exponential 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.