翻訳と辞書 Words near each other ・ Giovanni Tonoli ・ Giovanni Tonucci ・ Giovanni Torlonia, 1st Prince di Civitella-Cesi ・ Giovanni Tornabuoni ・ Giovanni Tortelli ・ Giovanni Toti ・ Giovanni Trapattoni ・ Giovanni Treccani ・ Giovanni Trigueros ・ Giovanni Tubino ・ Giovanni Tuccari ・ Giovanni Turba ・ Giovanni Ulisse Lucci ・ Giovanni Urbani ・ Giovanni Urbinati ・ Giovanni Vacca ・ Giovanni Vacca (doctor) ・ Giovanni Vailati ・ Giovanni Valentini ・ Giovanni Valentini (artist) ・ Giovanni Valentini (classical era composer) ・ Giovanni Valentino Gentile ・ Giovanni Valesi ・ Giovanni Valesio ・ Giovanni Valetti ・ Giovanni van Bronckhorst ・ Giovanni Varglien ・ Giovanni Vasanzio ・ Giovanni Vastola ・ Giovanni Vavassori 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 Giovanni Vacca ： ウィキペディア英語版 Giovanni Vacca Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science. Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin and became an assistant to Giuseppe Peano. In 1899 he studied, at Hanover, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin. He took private lessons of Chinese and continued to study it at the University of Florence. Vacca then traveled to China in 1907–8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947. The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number iteration for pi:〔G. Vacca. ''A new analytical expression for the number π and some historical considerations'', Bulletin of the American Mathematical Society (Ser. 2), 1910, vol.16, pp. 368–369〕 :$x\_0\; =\; i,\backslash quad\; x\_\; =\; \backslash frac2,\backslash qquad\backslash lim\_\; x\_n\; =\; \backslash frac2\backslash pi.$ The calculation efficiency of these formulas is significantly worse than of the modern Borwein's algorithm – they converge by only about half a decimal point with each iteration. Vacca published his two major contributions to mathematics in 1910 and 1926, on series expansion (later named Vacca series) of the Euler constant. They are, respectively :$$ \begin \gamma &=& \sum_^\infty (-1)^k \frac = \tfrac12-\tfrac13 + 2\left(\tfrac14 - \tfrac15 + \tfrac16 - \tfrac17\right) + 3\left(\tfrac18 - \cdots - \tfrac1\right) + \cdots\\ \zeta(2) + \gamma &=& \sum_^\infty\left(\frac1 - \frac1\right) = \sum_^ \frac = \tfrac12 + \tfrac23 + \tfrac1\left(\tfrac15 + \tfrac26 + \tfrac37 + \tfrac48\right) + \tfrac1\left(\tfrac1 + \cdots + \tfrac6\right) + \cdots \end Vacca noted in 1910 that: :''There is some hope that this series can be of some use in the proof of the irrationality of $\backslash gamma$, a very difficult problem, proposed, but not resolved, in the Correspondence, recently published, between Hermite und Stieltjes.'' ==References== 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「Giovanni Vacca」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.