New posts in Euler Mascheroni Constant

Prime Zeta function at 1

How can I prove $\frac{\gamma}{2}=\int_{0}^{\infty}\frac{e^{-x^{2}}-e^{-x}}{x}\text{d}x$?

Integral representation of the Euler-Mascheroni constant involving $\pi$

Calculating a limit with trigonometric and quadratic function

How can we show that $\sum_{n=1}^{\infty}\left({x\over n}-\ln{n+x\over n}\right)=x\gamma+\ln(x!)?$

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

How to show $\int_{0}^{\infty}{{\gamma+\ln x\over e^x}}\cdot{1-\cos x\over x} \,\mathrm dx={1\over 2}\cdot{\pi-\ln 4\over 4}\cdot{\pi+\ln4\over 4}?$

Mathematica gives: $\int_{0}^{\infty}{\cos(x^n)-\cos(x^{2n})\over x}\cdot{\ln{x}}\mathrm dx={12\gamma^2-\pi^2\over 2(4n)^2}$

Real Analysis Methodologies to show $\gamma =2\int_0^\infty \frac{\cos(x^2)-\cos(x)}{x}\,dx$

Alternative approaches to showing that $\gamma=\int_0^\infty \left(\frac{1}{1+x^a}-\frac{1}{e^x}\right)\,\frac1x\,dx$, $a>0$