Angular integrals and radial recurrence relations for two-electron matrix elements in Hylleraas coordinates

General formulas are obtained for the reduction of a wide class of two-electron matrix elements in Hylleraas coordinates to finite sums of radial integrals for states of arbitrary angular momentum. Multipole transition integrals and the Breit interaction are treated as special cases. A number of recurrence relations are derived for radial integrals containing PL(cosθ) (where cosθ=^r₁·^r₂) in terms of radial integrals containing lower-order Legendre polynomials. The results are well suited to computer implementation.