EDB — 0D6

[0D6]Topics:Euler-Mascheroni constant.Prerequisites:[211]↺↻.

Show that the limit

exists and is finite. This $𝛾$ is called Costante di Eulero - Mascheroni. It can be defined in many different ways (see the previous link) including

where the parentheses $\lfloor \cdot \rfloor$ indicate the floor function $\lfloor x\rfloor \stackrel{.}{=}max\{n\in \mathbb{Z}:n\le x\}$. In the image 1 the constant $𝛾$ is the blue area.

Image by William Demchick, Creative Commons Attribution 3.0 Unported License, taken from wikipedia.