For questions related to Euler's constant $\gamma$, which is defined to be the limiting difference between the natural logarithm and the harmonic series.

Euler's constant, also called the Euler-Mascheroni constant and typically denoted $\gamma$, is defined to be the limiting difference between the natural logarithm and the harmonic numbers:

$$\gamma=\lim_{n \to \infty}H_n-\log n$$ where

$$H_n=1+\frac{1}{2}+\cdots+\frac{1}{n}$$

Euler's constant arises in analysis and number theory, in part due to its connections with the gamma and zeta functions.

Note this is not the same as Euler's number $e$, defined by $e:=\sum_{n=0}^{\infty}\frac{1}{n!}$. Questions about this number should use the tag eulers-number-e.

Source: the Wikipedia article on the Euler-Mascheroni constant.