# Euler-Mascheroni constant

 Importance: High ✭✭✭
 Author(s):
 Subject: Number Theory » Analytic Number Theory
 Keywords: constant Euler irrational Mascheroni rational transcendental
 Recomm. for undergrads: no
 Posted by: Juggernaut on: July 19th, 2011

\begin{question} Is Euler-Mascheroni constant an transcendental number? \end{question}

Let $\gamma:=\lim_{n\rightarrow\infty}\left(\sum_{k=1}^n\left(\frac{1}{k}\right)-\ln(n)\right)$. The number $\gamma$ has not been proved algebraic or transcendental. In fact, it is not even known whether $\gamma$ is irrational.

### Euler-Masqueroni contant

If n = 2^k then log(n) is irrational. But Sum{1/k} is ever rational . Then Sum{1/k} - Log(n) is ever irrational.. Ludovicus

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