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In mathematics, the binomial series is the Maclaurin series for the function given by , where is an arbitrary complex number. Explicitly, : and the binomial series is the power series on the right hand side of (1), expressed in terms of the (generalized) binomial coefficients : == Special cases == If α is a nonnegative integer ''n'', then the (''n'' + 2)th term and all later terms in the series are 0, since each contains a factor (''n'' − ''n''); thus in this case the series is finite and gives the algebraic binomial formula. The following variant holds for arbitrary complex ''β'', but is especially useful for handling negative integer exponents in (1): : To prove it, substitute ''x'' = −''z'' in (1) and apply a binomial coefficient identity, which is, :. 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「binomial series」の詳細全文を読む スポンサード リンク
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