In this article two-loop QED corrections to the muon decay and corrections of
order $\alpha_s^2$ to the semileptonic decay of the bottom quark are
considered. We compute the imaginary part of the four-loop diagrams
contributing to the corresponding fermion propagator in the limit of small
external momentum. The on-shell condition is obtained with the help of a
conformal mapping and Pad\'e approximation. Via this method we confirm the
existing results by an independent calculation.