Euler-Mascheroni constant

Etymology
Named after mathematicians (1707—1783) and  (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

 * 1)  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, $$\textstyle\gamma = \lim_{n\to\infty}\left(-\ln n + \sum_{k=1}^n \frac 1 k \right)=\int_1^\infty\left(-\frac 1 x+\frac 1{\lfloor x\rfloor}\right)\,dx$$, where $$\lfloor x\rfloor$$ represents the floor function.

Translations

 * German: Euler-Mascheroni-Konstante, Eulersche Konstante
 * Italian: costante di Eulero-Mascheroni