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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 Fransén–Robinson constant ： ウィキペディア英語版 Fransén–Robinson constant The Fransén–Robinson constant, sometimes denoted ''F'', is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive ''x'' axis. That is, :$F\; =\; \backslash int\_^\backslash infty\; \backslash frac\backslash ,\; \backslash mathrmx.$ The Fransén–Robinson constant has numerical value ''F'' = 2.8077702420285... , with the continued fraction representation (1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ... ) . Its proximity to Euler's number ''e'' = 2.71828... follows from the fact that the integral can be approximated by :$F\; \backslash approx\; \backslash sum\_^\backslash infty\; \backslash frac\; =\; \backslash sum\_^\backslash infty\; \backslash frac,$ the standard series for ''e''. The difference is given by :$F\; =\; e\; +\; \backslash int\_0^\backslash infty\; \backslash frac\backslash ,\; \backslash mathrmx$ and also by :$F\; =\; e\; +\; \backslash frac\; \backslash int\_^\; e^\; e^\backslash theta.$ The Fransén–Robinson constant can also be expressed using the Mittag-Leffler function as the limit :$F\; =\; \backslash lim\_\; \backslash alpha\; E\_(1).$ It is however unknown whether ''F'' can be expressed in closed form in terms of other known constants. A fair amount of effort has been made to calculate the numerical value of the Fransén–Robinson constant with high accuracy. The value was computed to 36 decimal places by Herman P. Robinson using 11-point Newton–Cotes quadrature, with 65 digits by A. Fransén using Euler–Maclaurin summation, and with 80 digits by Fransén and S. Wrigge using Taylor series and other methods. William A. Johnson computed 300 digits, and Pascal Sebah was able to compute 600 digits using Clenshaw–Curtis integration. ==References== * * * * (【引用サイトリンク】last1=Finch ) * * * (【引用サイトリンク】last1=Fransen ) 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「Fransén–Robinson constant」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.