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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 : It is also often written as . 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 : which goes to the plain derivative, → ''d''⁄''dx'', as ''q'' → 1. It is manifestly linear, : It has product rule analogous to the ordinary derivative product rule, with two equivalent forms : Similarly, it satisfies a quotient rule, : There is also a rule similar to the chain rule for ordinary derivatives. Let . Then : 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
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