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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 Gauss's continued fraction ： ウィキペディア英語版 Gauss's continued fraction In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several important elementary functions, as well as some of the more complicated transcendental functions. ==History== Lambert published several examples of continued fractions in this form in 1768, and both Euler and Lagrange investigated similar constructions,〔Jones & Thron (1980) p. 5〕 but it was Carl Friedrich Gauss who utilized the clever algebraic trick described in the next section to deduce the general form of this continued fraction, in 1813.〔C. F. Gauss (1813), (''Werke'', vol. 3 ) pp. 134-138.〕 Although Gauss gave the form of this continued fraction, he did not give a proof of its convergence properties. Bernhard Riemann〔B. Riemann (1863), "Sullo svolgimento del quoziente di due serie ipergeometriche in frazione continua infinita" in ''Werke''. pp. 400-406. (Posthumous fragment).〕 and L.W. Thomé〔L. W. Thomé (1867), "Über die Kettenbruchentwicklung des Gauß'schen Quotienten ...," ''Jour. für Math.'' vol. 67 pp. 299-309.〕 obtained partial results, but the final word on the region in which this continued fraction converges was not given until 1901, by Edward Burr Van Vleck.〔E. B. Van Vleck (1901), "On the convergence of the continued fraction of Gauss and other continued fractions." ''Annals of Mathematics'', vol. 3 pp. 1-18.〕 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「Gauss's continued fraction」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.