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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 Q-derivative ： ウィキペディア英語版 Q-derivative In mathematics, in the area of combinatorics, the ''q''-derivative, or Jackson derivative, is a ''q''-analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's ''q''-integration. ==Definition== The ''q''-derivative of a function ''f''(''x'') is defined as :$\backslash left(\backslash frac\backslash right)\_q\; f(x)=\backslash frac.$ It is also often written as $D\_qf(x)$. The ''q''-derivative is also known as the Jackson derivative. Formally, in terms of Lagrange's shift operator in logarithmic variables, it amounts to the operator :$D\_q=\; \backslash frac\; ~\; \backslash frac\; ~,$ which goes to the plain derivative, → ''d''⁄''dx'', as ''q'' → 1. It is manifestly linear, :$\backslash displaystyle\; D\_q\; (f(x)+g(x))\; =\; D\_q\; f(x)\; +\; D\_q\; g(x)~.$ It has product rule analogous to the ordinary derivative product rule, with two equivalent forms :$\backslash displaystyle\; D\_q\; (f(x)g(x))\; =\; g(x)D\_q\; f(x)\; +\; f(qx)D\_q\; g(x)\; =\; g(qx)D\_q\; f(x)\; +\; f(x)D\_q\; g(x).$ Similarly, it satisfies a quotient rule, :$\backslash displaystyle\; D\_q\; (f(x)/g(x))\; =\; \backslash frac,\backslash quad\; g(x)g(qx)\backslash neq\; 0.$ There is also a rule similar to the chain rule for ordinary derivatives. Let $g(x)\; =\; c\; x^k$. Then :$\backslash displaystyle\; D\_q\; f(g(x))\; =\; D\_(f)(g(x))D\_q(g)(x).$ The eigenfunction of the ''q''-derivative is the ''q''-exponential ''eq''(''x''). 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「Q-derivative」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.