Taylor expansion at $\mu=0$ and computations at imaginary values of the chemical potential are the two most popular approaches to tackle the sign problem in finite-density lattice QCD. The two methods are obviously related. In particular, the Taylor coefficients are often reconstructed from the data obtained at imaginary $\mu$. In the context of the Bielefeld-Parma collaboration, we have been generating data which fed our multi-point Padé analysis of the QCD phase diagram. We report on our studies on the different techniques to compute the Taylor coefficients at $\mu=0$.