Riemann and the logarithmic derivatives of zeta

In one of his posthumous papers, conserved in Göttingen, Riemann considers the derivatives of $\log \zeta (s)$ at the point $1\mathrm{/}2$, 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 $$\frac{{\zeta }^{\mathrm{\prime }}(\frac{1}{2})}{\zeta (\frac{1}{2})}=\frac{\pi }{4}+\frac{\gamma }{2}+\frac{\log (8\pi )}{2},\frac{{\zeta }^{\mathrm{\prime }\mathrm{\prime }}(\frac{1}{2})}{\zeta (\frac{1}{2})}-(\frac{{\zeta }^{\mathrm{\prime }}(\frac{1}{2})}{\zeta (\frac{1}{2})}{)}^2=8-\frac{{\pi }^2}{4}-2G+2\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{\alpha }_n^2}$$