Consider the following implementation of the complex square root:

f[z_]:=Sqrt[(z - I)/(z + I)]*(z + I); 

This implementation has branch points at $ \lambda=\pm i$ and a (vertical) branch cut connecting them.

Then

g[z_]:=Sinc[f[z]]; 

(recalling $ \mathrm{sinc}(x)=\sin(x)/x$ ) has no branch cut and it is analytic on the entire complex plane, and admits power series expansions at $ \lambda=\pm i$ .

Indeed, using Mathematica 11.0.0 (Mac OS 10.10.5) gives:

Series[Sinc[rhofun[z]], {z, I, 4}] 

$ 1-\frac{1}{3} i (z-i)-\frac{1}{5} (z-i)^2+\frac{11}{315} i (z-i)^3+\frac{61 (z-i)^4}{5670}+O\left((z-i)^5\right)$

and

SeriesCoefficient[Sinc[rhofun[z]], {z, I, 4}] 

gives $ \frac{61}{5670}$ .

Now, using Mathematica 11.1.1 (both on Mac OS 10.12 Sierra and Linux Ubuntu 16 LTS)

Series[Sinc[rhofun[z]], {z, I, 4}] 

returns

Series[Sinc[rhofun[z]], {z, I, 4}] 

and

SeriesCoefficient[Sinc[rhofun[z]], {z, I, 4}] 

returns

SeriesCoefficient[Sinc[rhofun[z]], {z, I, 4}]. 

So neither of these stock functions work in properly in Mathematica 11.1.1. Does anyone know what is going on? Will this be fixed? They worked properly even in Mathematica 9 and also in Mathematica 11.0.0

Besides any information, I’d also appreciate if anyone has a workaround for this.