Definition of Euler's constant in US English:

Euler's constant


  • 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.’
    • ‘In Adnotationes ad calculum integrale Euleri Mascheroni calculated Euler's constant to 32 decimal places.’
    • ‘He investigated the series and calculated Euler's constant to 15 decimal places.’
    • ‘For example he computed Euler's constant to 1271 decimal places and published the result in 1962.’


Mid 19th century: named after L. Euler (see Euler, Leonhard).