On the analytic computation of massless propagators in dimensional regularization

We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ and show examples at four and more loops. Further we prove that all coefficients of the $\varepsilon$-expansion of these integrals are rational linear combinations of multiple zeta values and in some cases possibly also alternating Euler sums.