翻訳と辞書 Words near each other ・ Geležinis Vilkas ・ GELF ・ Gelfand ・ Gelfand pair ・ Gelfand representation ・ Gelfand ring ・ Gelfand–Graev representation ・ Gelfand–Kirillov dimension ・ Gelfand–Mazur theorem ・ Gelfand–Naimark theorem ・ Gelfand–Naimark–Segal construction ・ Gelfand–Raikov theorem ・ Gelfand–Shilov space ・ Gelfand–Zeitlin integrable system ・ Gelfingen ・ Gelfond's constant ・ Gelfond–Schneider constant ・ Gelfond–Schneider theorem ・ Gelgaudiškis ・ Gelgaudiškis Manor ・ Gelgel ・ Gelgel, Indonesia ・ Gelgelab ・ Gelgelab, Ardabil ・ Gelgia (river) ・ GelGreen ・ Gelgéis ・ Geli ・ Geli (software) ・ Geli Ali Beg Waterfall 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 Gelfond's constant ： ウィキペディア英語版 Gelfond's constant In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is ''e'', that is, ''e'' raised to the power . Like both ''e'' and , this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond–Schneider theorem, noting the fact that :$e^\backslash pi\; =\; (e^)^\; =\; (-1)^,$ where ''i'' is the imaginary unit. Since −''i'' is algebraic but not rational, ''e'' is transcendental. The constant was mentioned in Hilbert's seventh problem. A related constant is $2^\backslash sqrt$, known as the Gelfond–Schneider constant. The related value  + ''e'' is also irrational. ==Numerical value== The decimal expansion of Gelfond's constant begins :$e^\backslash pi\; \backslash approx\; 23.14069263277926900572908636794854738\backslash dots\backslash ,.$ If one defines $\backslash scriptstyle\; k\_0\backslash ,=\backslash ,\backslash tfrac=\backslash frac\}$ for $n\; >\; 0$ then the sequence :$(4/k\_)^\{2^\{1-n\}\}$ converges rapidly to $e^\backslash pi$. 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「Gelfond's 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.