|
|
|
|
|
Euler-mascheroni ConstantThe 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: -
\sum_{k=1}^n \frac{1}{k} - \ln(n) \right)=\int_1^\infty\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx 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, among other places, in: It is named for the mathematicians Leonhard Euler and Lorenzo Mascheroni. External link
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|