  Convergence properties of Taylor expansions of observables, which are also
used in lattice QCD calculations at non-zero chemical potential, are analyzed
in an effective N_f = 2+1 flavor Polyakov-quark-meson model. A recently
developed algorithmic technique allows the calculation of higher-order Taylor
expansion coefficients in functional approaches. This novel technique is for
the first time applied to an effective N_f = 2+1 flavor Polyakov-quark-meson
model and the findings are compared with the full model solution at finite
densities. The results are used to discuss prospects for locating the QCD phase
boundary and a possible critical endpoint in the phase diagram.
