Home » Subject » Number Theory » Analytic N.T.

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
Question   Is Euler-Mascheroni constant an transcendental number?

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.

add new comment

Euler-Masqueroni contant

On January 21st, 2013 Anonymous says:

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

reply

Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.