The Euler-Mascheroni constant, denoted by the symbol γ (gamma), is a mathematical constant that appears in various areas of number theory and analysis. Its approximate value is 0.57721, and it is defined as the limiting difference between the harmonic series and the natural logarithm. Specifically, it can be expressed as the limit of the difference between the sum of the first n natural numbers and the natural logarithm of n as n approaches infinity. This constant is named after the mathematicians Leonhard Euler and Carlo Mascheroni, who studied its properties in the 18th century. The Euler-Mascheroni constant is significant in various mathematical contexts, including integrals, series, and asymptotic analysis, and it appears in formulas related to the distribution of prime numbers and the Riemann zeta function.