Multiloop calculations in HQET

Recently, algorithms for calculating three-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. The algorithms (based on integration by parts recurrence relations) reduce an arbitrary diagram to a combination of a finite number of basis integrals. Here, I discuss various ways of calculating non-trivial bases integrals, either exactly or as expansions in ε. Some integrals of the two classes are related to each other by inversion, which provides a useful cross-check.