翻訳と辞書 Words near each other ・ Abell 33 ・ Abell 36 ・ Abell 370 ・ Abell 383 ・ Abell 39 ・ Abell 400 ・ Abell 478 ・ Abell 520 ・ Abell 665 ・ Abel's irreducibility theorem ・ Abel's Island ・ Abel's Island (film) ・ Abel's sum formula ・ Abel's summation formula ・ Abel's test ・ Abel's theorem ・ Abel, Alabama ・ Abel, King of Denmark ・ Abel, Lord of Langeland ・ Abel-beth-maachah ・ Abel-cheramim ・ Abel-Dominique Boyé ・ Abel-François Villemain ・ Abel-meholah ・ Abel-mizraim ・ Abel-Nicolas Bergasse Dupetit Thouars ・ Abel-Steinberg-Winant Trio ・ Abel/Kein ・ Abela ・ Abelag Aviation Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Abel's theorem ： ウィキペディア英語版 Abel's theorem In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel. ==Theorem== Let ''a'' = be any sequence of real or complex numbers and let :$G\_a(z)\; =\; \backslash sum\_^\; a\_k\; z^k\backslash !$ be the power series with coefficients ''a''. Suppose that the series $\backslash sum\_^\backslash infty\; a\_k\backslash !$ converges. Then :$\backslash lim\_\; G\_a(z)\; =\; \backslash sum\_^\backslash infty\; a\_k,\backslash qquad\; ($ *)\! where the variable ''z'' is supposed to be real, or, more generally, to lie within any ''Stolz angle'', that is, a region of the open unit disk where : $|1-z|\backslash leq\; M(1-|z|)\; \backslash ,$ for some ''M''. Without this restriction, the limit may fail to exist: for example, the power series :$\backslash sum\_\; \backslash frac\}\; n$ converges to 0 at ''z'' = 1, but is unbounded near any point of the form ''e''i/3''n'', so the value at ''z'' = 1 is not the limit as ''z'' tends to 1 in the whole open disk. Note that $G\_a(z)$ is continuous on the real closed interval (''t'' ) for ''t'' < 1, by virtue of the uniform convergence of the series on compact subsets of the disk of convergence. Abel's theorem allows us to say more, namely that $G\_a(z)$ is continuous on (). 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「Abel's theorem」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.