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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.
‘In Adnotationes ad calculum integrale Euleri Mascheroni calculated Euler's constant to 32 decimal places.’
‘It's been called the logarithmic constant, Napier's number, Euler's constant, and the natural logarithmic base.’
‘For example he computed Euler's constant to 1271 decimal places and published the result in 1962.’
‘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.’
Origin
Mid 19th century: named after L. Euler (see Euler, Leonhard).