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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 Abel function ： ウィキペディア英語版 Abel equation The Abel equation, named after Niels Henrik Abel, is a type of functional equations which can be written in the form :$f(h(x))\; =\; h(x\; +\; 1)$ or, equivalently, :$\backslash alpha(f(x))=\backslash alpha(x)+1$ and controls the iteration of   . ==Equivalence== These equations are equivalent. Assuming that is an invertible function, the second equation can be written as :$\backslash alpha^(\backslash alpha(f(x)))=\backslash alpha^(\backslash alpha(x)+1)\backslash ,\; .$ Taking , the equation can be written as ::$f(\backslash alpha^(y))=\backslash alpha^(y+1)\backslash ,\; .$ For a function assumed to be known, the task is to solve the functional equation for the function , possibly satisfying additional requirements, such as . The change of variables , for a real parameter , brings Abel's equation into the celebrated Schröder's equation, . The further change into Böttcher's equation, . The Abel equation is a special case of (and easily generalizes to) the translation equation,〔Aczél, János, (1966): ''Lectures on Functional Equations and Their Applications'', Academic Press, reprinted by Dover Publications, ISBN 0486445232 .〕 :$\backslash omega(\; \backslash omega(x,u),v)=\backslash omega(x,u+v)\; ~,$ e.g., for $\backslash omega(x,1)=\; f(x)$, :$\backslash omega(x,u)=\; \backslash alpha^(\backslash alpha(x)+u)$.     (Observe .) 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「Abel equation」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.