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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 Tangent half-angle substitution ： ウィキペディア英語版 Tangent half-angle substitution In integral calculus, the tangent half-angle substitution is a substitution used for finding antiderivatives, and hence definite integrals, of rational functions of trigonometric functions. No generality is lost by taking these to be rational functions of the sine and cosine. Michael Spivak wrote that "The world's sneakiest substitution is undoubtedly" this technique.〔Michael Spivak, ''Calculus'', Cambridge University Press, 2006, pages 382–383.〕 == Euler and Weierstrass == Various books call this the Weierstrass substitution, after Karl Weierstrass (1815 – 1897), without citing any occurrence of the substitution in Weierstrass' writings,〔Gerald L. Bradley and Karl J. Smith, ''Calculus'', Prentice Hall, 1995, pages 462, 465, 466〕〔Christof Teuscher, ''Alan Turing: Life and Legacy of a Great Thinker'', Springer, 2004, pages 105–6〕〔James Stewart, ''Calculus: Early Transcendentals'', Brooks/Cole, Apr 1, 1991, page 436〕 but the technique appears well before Weierstrass was born, in the work of Leonhard Euler (1707 – 1783).〔Leonhard Euler, ''Institutiionum calculi integralis volumen primum'', 1768, E342, Caput V, paragraph 261. See (http://www.eulerarchive.org/ )〕 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「Tangent half-angle substitution」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.