Master formulas for two- and three-center one-electron integrals involvingcartesian GTO, STO, and BTO

As a first application of the shift operators method we derive master formu las for the two- and three-center one-electron integrals involving Gaussian s, Slater, and Bessel basis functions. All these formulas have a common str ucture consisting in linear combinations of polynomials of differences of n uclear coordinates. Whereas the polynomials are independent of the type (GT O, BTO, or STO) of basis functions, the coefficients depend on both the cla ss of integral (overlap, kinetic energy, nuclear attraction) and the type o f basis functions. We present the general expression of polynomials and coe fficients as well as the recurrence relations for both the polynomials and the whole integrals. Finally, we remark on the formal and computational adv antages of this approach.