  The computation of master integrals from their differential equations
requires boundary values to be supplied by an independent method. These
boundary values are often desired at singular kinematical points. We
demonstrate how the auxiliary mass flow technique can be extended to compute
the expansion coefficients of master integrals in a singular limit in an
analytical manner, thereby providing these boundary conditions. To illustrate
the application of the method, we re-compute the phase space integrals relevant
to initial-final antenna functions at NNLO, now including higher-order terms in
their $\epsilon$-expansion in view of their application in third-order QCD
corrections.
