\begin{definition}[Definition:Euler-Mascheroni Constant]
The '''Euler-Mascheroni constant''' $\gamma$ is the real number that is defined as:
{{begin-eqn}}
{{eqn | l = \gamma
      | o = :=
      | r = \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}
}}
{{eqn | r = \lim_{n \mathop \to +\infty} \paren {H_n - \ln n}
}}
{{end-eqn}}
where $H_n$ is the harmonic series and $\ln$ is the natural logarithm.
\end{definition}