The auxiliary functions Q(nn)(q), (p,pt) and G(-nn)(q), (p(a),p,pt) which are used in our previous paper [Guseinov, I. I.; Mamedov, B. A. Int J Quantum Chem 2001, 81, 117] for the computation of multicenter electron-repulsion integrals over Slater-type orbitals (STOs) are discussed in detail, and the method is given for their numerical computation. The present method is suitable for all values of the parameters p(a),p, and pt. Three- and four-center electron-repulsion integrals are calculated for extremely large quantum numbers using relations for auxiliary functions obtained in this paper. (C) 2002 John Wiley Sons, Inc.