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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 seriesRead more