EulerMascheroniConstant

The Euler-Mascheroni constant, often denoted by $\gamma$, is a mathematical constant that appears in various branches of mathematics, including calculus and number theory. It is defined as the limiting difference between the harmonic series and the natural logarithm:

$$\gamma = \lim_{n \to \infty} \left(1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \ldots + \frac{1}{n} - \ln(n)\right)$$

The numerical value of the Euler-Mascheroni constant is approximately 0.57721566490153286060. This number is named after the Swiss mathematician Leonhard Euler and the Italian mathematician Lorenzo Mascheroni.

The Euler-Mascheroni constant pops up in several mathematical expressions, particularly in integrals and series, and also in the definition of the Riemann zeta function, which connects it with the Riemann Hypothesis, one of the most famous unsolved problems in mathematics.