Euler's constant

The Euler-Mascheroni constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series and the natural logarithm:

γ = lim_n→∞ ( (Σ_{k=1 to n} 1/k) - ln(n) )

Intriguingly, the constant is also given by:

γ = - ∫₀^∞ ln(x)/e^x dx

Its value is approximately

γ ≈ 0.57721566...

It is not known whether γ is rational or not.