翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Euler constant : ウィキペディア英語版
Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter (\gamma).
It is defined as the limiting difference between the harmonic series and the natural logarithm:
:\begin
\gamma &= \lim_ \left(
-\ln(n) + \sum_^n \frac \right)\\
&=\int_1^\infty\left(-\right)\,dx.
\end
Here, \lfloor x\rfloor represents the floor function.
The numerical value of the Euler–Mascheroni constant, to 50 decimal places, is
: .
==History==
The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled ''De Progressionibus harmonicis observationes'' (Eneström Index 43). Euler used the notations ''C'' and ''O'' for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations ''A'' and ''a'' for the constant. The notation \gamma appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time perhaps because of the constant's connection to the gamma function. For example, the German mathematician Carl Anton Bretschneider used the notation \gamma in 1835〔Carl Anton Bretschneider: ''Theoriae logarithmi integralis lineamenta nova'' (13 October 1835), Journal für die reine und angewandte Mathematik 17, 1837, pp. 257–285 (in Latin; "''γ'' = ''c'' = 0,577215 664901 532860 618112 090082 3.." on (p. 260 ))〕 and Augustus De Morgan used it in a textbook published in parts from 1836 to 1842.〔Augustus De Morgan: ''The differential and integral calculus'', Baldwin and Craddock, London 1836–1842 ("''γ''" on (p. 578 ))〕

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「Euler–Mascheroni 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.