Encyclopedia > Euler-Mascheroni constant

  Article Content

Euler-Mascheroni 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:

<math>\gamma = \lim_{n \rightarrow \infty } \left(
\sum_{k=1}^n \frac{1}{k} - \ln(n) \right)</math>

Intriguingly, the constant is also given by the integral:

<math>\gamma = - \int_0^\infty { \ln(x) \over e^x } dx </math>

where ln(x) is the natural logarithm of x.

Its value is approximately

γ ≈ 0.57721566...

It is not known whether γ is a rational number or not. However, continued fraction analysis shows that if γ is rational, it has a large denominator.

The Euler-Mascheroni constant appears in



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Bullying

... any period of time without a legitimate basis of authority. The first to have the title of "Tyrant" was Pisistratus in 560 BC. In modern times Tyrant has come to ...

 
 
 
This page was created in 25.5 ms