Life of $\Pi$

The heavy-quark contribution to the polarisation function $\Pi$ at higher perturbative orders is presently only known approximately. We scrutinise the accuracy of state-of-the-art Padé approximations at three- and four-loop order. At three loops, we present for the first time the exact result for general kinematics and compare to the best Padé estimate. At four loops, we calculate the fourth (inverse) moment of the heavy-quark vacuum polarisation in order to test the prediction for this moment based on Padé approximation