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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 (). It is defined as the limiting difference between the harmonic series and the natural logarithm: : Here, 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 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 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
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