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