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

... the Unseen University University of Utah Union University[?] This is a disambiguation page; that is, one that just points to other pages that might otherwise ...

This page was created in 22.9 ms