In earlier work, Li, Ahuja, Harrison, and Hunt have calculated the collision-induced polarizability Δα of a pair of hydrogen molecules at CCSD(T) level with an aug-cc-pV5Z basis, for 178 relative orientations of the pair, with the bond length in each molecule fixed at r = 1.449 a.u. Here we present new results from an expansion of the second-rank tensor components of Δα as series in the spherical harmonics of the molecular orientation angles and the orientation angles of the intermolecular vector. The coefficients in this expansion depend on the separation R between the molecules. We compare the ab initio coefficients with predictions from long-range perturbation theory, including the dipole-induced-dipole interactions at first and second order, higher-multipole induction, effects of nonuniform local fields, hyperpolarization, and van der Waals dispersion. Li and Hunt have derived equations for the long-range coefficients complete to order R^-6, using spherical-tensor methods developed by Bancewicz, Głaz, and Kielich for collision-induced light scattering by centrosymmetric linear molecules. We also give new results here for the van der Waals dispersion terms in both isotropic and anisotropic polarizability coefficients. We have calculated these coefficients by 64-point Gauss-Legendre quadrature, using the H₂ polarizabilities and hyperpolarizabilities at imaginary frequencies computed by Bishop and Pipin, with explicitly correlated wave functions for isolated H₂ molecules. We show that the ab initio values for the larger anisotropic polarizability coefficients converge to the predictions of the long-range theory, as the separation R between the molecules increases. The coefficients computed ab initio have been used by Gustafsson, Frommhold, Li, and Hunt to calculate the depolarized collision-induced roto-translational Raman spectra of hydrogen gas at 36 K and 50 K out to 800 cm^-1, and at 296 K out to 300 cm^-1. The general features of the experimental spectra are well reproduced, although the calculated intensities are ~30% too large over much of the frequency range.