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eu·ler's con·stant

Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (γ). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log : {\displaystyle \log :} γ = lim n → ∞ ( − log ⁡ n + ∑ k = 1 n 1 k ) = ∫ 1 ∞ ( − 1 x + 1 ⌊ x ⌋ ) d x . {\displaystyle {\begin{aligned}\gamma &=\lim _{n\to \infty }\left(-\log n+\sum _{k=1}^{n}{\frac {1}{k}}\right)\\[5px]&=\int _{1}^{\infty }\left(-{\frac {1}{x}}+{\frac {1}{\lfloor x\rfloor }}\right)\,dx.\end{aligned}}} Here, ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } represents the floor function. The numerical value of Euler's constant, to 50 decimal places, is: 0.57721566490153286060651209008240243104215933593992... 

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