The hypergeometric function$\ _2F_1(a,b;c;z)$ has a branch point at $z=1$. How do I compute the discontinuity around the point? In particular, how do I compute the following?
$$\lim_{\epsilon\rightarrow 0^+} \ _2F_1(1,b;b+1;1+\epsilon)-\ _2F_1(1,b;b+1;1-\epsilon)$$
Mathematica says that it is $-ib\pi$.