  Calculations of the leading quantum electrodynamics effects in few electron
systems involve singular matrix elements of the inter-electronic distances of
the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the
nonrelativistic wave function is represented with a Hylleraas basis
representation are studied. Recursion relations for various powers of the
electron coordinates and the master integrals are derived in a form suited for
high precision numerical evaluations.
