Постоянная Эйлера — Маскерони: различия между версиями

* <math>2\gamma = \lim\limits_{z\to 0} \frac1{z}\left\{\frac1{\Gamma(1+z)} - \frac1{\Gamma(1-z)} \right\}</math>
* <math> \frac{\pi^2}{3\gamma^2} = \lim_{z\to 0} \frac1{z}\left\{\frac1{\Psi(1-z)} - \frac1{\Psi(1+z)} \right\}.</math>
* <math> \gamma = \ln\pi - 4\ln\Gamma(\tfrac34) + \frac4{\pi}\sum_{k=1}^{\infty}(-1)^{k+1}\frac{\ln(2k+1)}{2k+1}.</math>
* <math> \gamma = \ln\pi - 4\ln\Gamma(\tfrac34) + \frac4{\pi}\sum_{k=1}^{\infty}(-1)^{k+1}\frac{\ln(2k+1)}{2k+1}.</math>
* <math> e^{-\gamma} = \lim\limits_{x\to\infty}\ln x\prod\limits_{p\leqslant x}\left(1-\frac{1}{p}\right).</math>