# Euler's Constant

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## Euler's constant

[′ȯi·lərz ¦kän·stənt] (mathematics)

The limit as

*n*approaches infinity, of 1 + 1/2 + 1/3 + ⋯ + 1/*n*- ln*n*, equal to approximately 0.5772. Denoted γ. Also known as Mascheroni's constant.## Euler’s Constant

(or Mascheroni’s constant), the limit

which was considered by L. Euler in 1740. Euler gave a number of representations for *C* in the form of series and integrals; for example,

where ζ(*s*) is the zeta function. Euler’s constant is encountered in the theory of various classes of special functions, such as the gamma function. It remains unknown whether Euler’s constant is an irrational number.