Euler-Mascheroni Constant

analysis

Definition

Euler-Mascheroni Constant

The Euler-Mascheroni constant, named after Leonhard Euler and Lorenzo Mascheroni, is a constant defined as the limiting difference between the harmonic series and the natural logarithm:

$$\begin{array}{rl}\gamma & =\underset{n\to \infty }{\lim }\left(-\ln n+\sum _{k=1}^n\frac{1}{k}\right)\\ & ={\int }_1^{\infty }\left(-\frac{1}{x}+\frac{1}{\lfloor x\rfloor }\right)dx\\ & \approx 0.5772156649\end{array}$$