Symbols:Greek/Gamma/Euler-Mascheroni Constant

From ProofWiki
Jump to navigation Jump to search

The Euler-Mascheroni Constant

$\gamma$


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

\(\displaystyle \gamma\) \(:=\) \(\displaystyle \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}\)
\(\displaystyle \) \(=\) \(\displaystyle \lim_{n \mathop \to +\infty} \paren {H_n - \ln n}\)

where $H_n$ is the harmonic series and $\ln$ is the natural logarithm.


The $\LaTeX$ code for \(\gamma\) is \gamma .