# 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:

Intriguingly, the constant is also given by the

integral:

Its value is approximately

- γ ≈ 0.577215664901532860606512090082402431042159335 9399235988057672348848677267776646709369470632917467495...

It is not known whether γ is a

rational number or not. However,

continued fraction analysis shows that if γ is rational, its denominator has more than 10,000 digits.

The Euler-Mascheroni constant appears in

- a product formula for the Gamma function
- calculations of the digamma function

### External link

Euler-Mascheroni constant