Euler-Mascheroni constant

== English == === Etymology === Named after mathematicians Leonhard Euler (1707—1783) and Lorenzo Mascheroni (1750—1800). The origin of the notation γ is unclear: it may have been first used by either Euler or Mascheroni. It possibly reflects the constant's connection to the gamma function. === Proper noun === Euler-Mascheroni constant (mathematics) A constant, denoted γ and recurring in analysis and number theory, that is defined as the limiting difference between the harmonic series and the natural logarithm and has the approximate value 0.57721566. ==== Usage notes ==== Mathematically, γ = lim n → ∞ ( − ln ⁡ n + ∑ k = 1 n 1 k ) = ∫ 1 ∞ ( − 1 x + 1 ⌊ x ⌋ ) d x {\displaystyle \textstyle \gamma =\lim _{n\to \infty }\left(-\ln n+\sum _{k=1}^{n}{\frac {1}{k}}\right)=\int _{1}^{\infty }\left(-{\frac {1}{x}}+{\frac {1}{\lfloor x\rfloor }}\right)\,dx} , where ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } represents the floor function. ==== Synonyms ==== (mathematical constant): Euler's constant, gamma ==== Translations ==== === References ===