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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 Gregory's series ： ウィキペディア英語版 Gregory's series Gregory's series, also known as the Madhava–Gregory series or Leibniz's series, is an infinite Taylor series expansion of the inverse tangent function. It was discovered by the Indian mathematician Madhava of Sangamagrama (1350- 1410) and independently rediscovered and published in 1668 by James Gregory. It was rediscovered a few years later by Gottfried Leibniz, who obtained the Leibniz formula for π as the special case ''x'' = 1 of the Gregory series.〔(【引用サイトリンク】url=http://mathworld.wolfram.com/GregorySeries.html )〕 ==Definition== Gregory's series is defined as below: : $\backslash int\_0^x\; \backslash ,\; \backslash frac\; =\; \backslash arctan\; x\; =\; x\; -\; \backslash frac\; +\; \backslash frac\; -\; \backslash frac\; +\; \backslash cdots$ Compare with the series for sine, which is similar but has factorials in the denominator. 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「Gregory's series」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.