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A constant used in numerical analysis, approximately equal to 0.577216. It represents the limit of the series 1 + 1/2 + 1/3 + 1/4 + …1/n − (natural logarithm of n), as n tends to infinity. It is not known whether this is a rational number or not.
‘It's been called the logarithmic constant, Napier's number, Euler's constant, and the natural logarithmic base.’
‘This is Euler's constant, named after the famous Swiss mathematician Leonard Euler.’
‘He investigated the series and calculated Euler's constant to 15 decimal places.’
‘In Adnotationes ad calculum integrale Euleri Mascheroni calculated Euler's constant to 32 decimal places.’
‘For example he computed Euler's constant to 1271 decimal places and published the result in 1962.’
Origin
Mid 19th century: named after L. Euler (see Euler, Leonhard).