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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 P-adic exponential function ： ウィキペディア英語版 P-adic exponential function In mathematics, particularly ''p''-adic analysis, the ''p''-adic exponential function is a ''p''-adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function, named the ''p''-adic logarithm. ==Definition== The usual exponential function on C is defined by the infinite series :$\backslash exp(z)=\backslash sum\_^\backslash infty\; \backslash frac.$ Entirely analogously, one defines the exponential function on C''p'', the completion of the algebraic closure of Q''p'', by :$\backslash exp\_p(z)=\backslash sum\_^\backslash infty\backslash frac.$ However, unlike exp which converges on all of C, exp''p'' only converges on the disc : This is because ''p''-adic series converge if and only if the summands tend to zero, and since the ''n''! in the denominator of each summand tends to make them very large ''p''-adically, rather a small value of ''z'' is needed in the numerator. 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「P-adic exponential function」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.