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