Atomic Integrals Containing r23λ r31μ r12v

S states of atoms may be calculated to high precision by means of expansions containing correlation factors of the form rijν. Resulting integrals may be expressed as sums of auxiliary functions which are evaluated by algebraic methods. Explicit expressions, suitable for computer programing, are given for such integrals for three-electron atoms; these include integrals containing correlation factors with linked indices, r23λ r31μ r12ν, with any set of (integral) values λ, μ, ν. Expressions are based on an expansion of rijν in terms of Legendre polynomials in cosθij; coefficients of this expansion are represented by a conveniently evaluated formula and some numerical values are given. The expressions given here have been found quite convenient in preliminary calculations of lithium ground state.