Generalized x-ray scattering factors have been determined from the evaluation of Fourier transforms of atomic-orbital products. Self-consistent-field atomic orbitals for first-row atoms have been studied. Analytical scattering expressions for rapid evaluation on digital computers have been developed. Scattering factors from small GTO expansions have been compared with both Clementi and Huzinaga SCF atomic orbitals. For one-center orbital products, the three-set GTO atomic orbitals agree with full SCF scattering factors to within five parts per hundred or better; the four-set GTO expansions have relative differences of 1.5% or less. For the two-center scattering cases, three or more Gaussians per atomic orbital yield relative errors less than 1%. The generalized x-ray scattering factors can serve as basis functions in the analysis of charge densities from x-ray diffraction data.