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In mathematics, in the field of combinatorics, the ''q''-Vandermonde identity is a ''q''-analogue of the Chu–Vandermonde identity. Using standard notation for ''q''-binomial coefficients, the identity states that : The nonzero contributions to this sum come from values of ''j'' such that the ''q''-binomial coefficients on the right side are nonzero, that is, ==Other conventions== As is typical for ''q''-analogues, the ''q''-Vandermonde identity can be rewritten in a number of ways. In the conventions common in applications to quantum groups, a different ''q''-binomial coefficient is used. This ''q''-binomial coefficient, which we denote here by , is defined by : In particular, it is the unique shift of the "usual" ''q''-binomial coefficient by a power of ''q'' such that the result is symmetric in ''q'' and . Using this ''q''-binomial coefficient, the ''q''-Vandermonde identity can be written in the form : 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-Vandermonde identity」の詳細全文を読む スポンサード リンク
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