Riemann and the logarithmic derivatives of zeta

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some mathematicians. From that time I have been asked several times for references. So I decided to write this. Specially explaining the wonderful formulas \[\frac{\zeta'(\frac12)}{\zeta(\frac12)}=\frac{\pi}{4}+\frac{\gamma}{2}+\frac{\log(8\pi)}{2},\quad \frac{\zeta''(\frac12)}{\zeta(\frac12)}-\Bigl(\frac{\zeta'(\frac12)}{\zeta(\frac12)}\Bigr)^2=8-\frac{\pi^2}{4}-2G+2\sum_{n=1}^\infty\frac{1}{\alpha_n^2}\]