# integral representations of the Mascheroni constant

Mascheroni’s constant can be expressed by the following integrals:

 $\displaystyle\gamma$ $\displaystyle=$ $\displaystyle-\int_{0}^{1}\log(-\log x)\,dx$ $\displaystyle\gamma$ $\displaystyle=$ $\displaystyle-\int_{0}^{\infty}e^{-x}\log x\,dx$ $\displaystyle\gamma$ $\displaystyle=$ $\displaystyle\int_{0}^{\infty}\left({1\over e^{t}-1}-{1\over te^{t}}\right)\,dt$ $\displaystyle\gamma$ $\displaystyle=$ $\displaystyle\int_{0}^{\infty}\left({1\over t}-{1\over 1+t}-{1\over te^{t}}% \right)\,dt$
Title integral representations of the Mascheroni constant IntegralRepresentationsOfTheMascheroniConstant 2013-03-22 15:53:24 2013-03-22 15:53:24 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Theorem msc 40A25