Singular Hylleraas three-electron integrals

Calculations of the leading quantum electrodynamics effects in few-electron systems involve singular matrix elements of interelectronic distances of the form 1/r(i)(3) and 1/r(ij)(3). Integrals that result when the nonrelativistic wave function is represented by a Hylleraas basis 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.