$\log \left(x^2+\sqrt{1-x^2}\right)$有4个branch point
$$\left\{\pm1,\pm i \sqrt{\phi}\right\}\quad\phi=\frac{1}{2}(1+\sqrt{5})$$
我觉得这里$\pm1$是2次ramification point，而$\pm i \sqrt{\phi}$是logarithmic branch point，不知对不对？
en.wikipedia.org/wiki/Branch_point#Riemann_surfaces Let γ be a simple rectifiable loop in X around P. The ramification index of ƒ at P is
$\displaystyle e_{P}={\frac {1}{2\pi i}}\int _{\gamma }{\frac {f'(z)}{f(z)-f(P)}}\,dz.$
This integral is the number of times ƒ(γ) winds around the point Q. As above, P is a ramification point and Q is a branch point if eP > 1.
![XbXEd[1].png](data/attachment/forum/202406/03/185111kte1qkp33392ccyt.png "XbXEd[1].png")
