Mathematical and computational science issues in high precision Hylleraas-configuration interaction variational calculations: III. Four-electron integrals

The Hylleraas-configuration interaction (Hy-CI) four-electron correlated integrals and their associated X auxiliary integrals are discussed. We explore the feasibility of the use of recursive methods for the X auxiliary integrals for all the cases that arise in Hy-CI calculations. The question of calibrating the calculation of these integrals is discussed, as well as ways to improve the work. (paper)