Definition:Euler-Mascheroni Constant

The Euler-Mascheroni Constant $$\gamma$$ is the real number that is defined as:

$$\gamma \ \stackrel {\mathbf {def}} {=\!=} \ \lim_{n \to \infty} \left({\sum_{k=1}^n \frac 1 k - \ln n}\right)$$

The existence of this constant is demonstrated in Existence of Euler-Mascheroni Constant.

Its value is approximately $$0.55721 56649 01532 86060 6512 ...$$