We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.