  Spectral observations below Lyman-alpha are now obtained with the Cosmic
Origin Spectrograph (COS) on the Hubble Space Telescope (HST). It is therefore
necessary to provide an accurate treatment of the blue wing of the Lyman-alpha
line that enables correct calculations of radiative transport in DA and DBA
white dwarf stars. On the theoretical front, we very recently developed very
accurate H-He potential energies for the hydrogen 1s, 2s, and 2p states.
Nevertheless, an uncertainty remained about the asymptotic correlation of the
Sigma states and the electronic dipole transition moments. A similar difficulty
occurred in our first calculations for the resonance broadening of hydrogen
perturbed by collisions with neutral H atoms. The aim of this paper is twofold.
First, we clarify the question of the asymptotic correlation of the Sigma
states, and we show that relativistic contributions, even very tiny, may need
to be accounted for a correct long-range and asymptotic description of the
states because of the specific 2s 2p Coulomb degeneracy in hydrogen. This
effect of relativistic corrections, inducing small splitting of the 2s and 2p
states of H, is shown to be important for the Sigma-Sigma$ transition dipole
moments in H-He and is also discussed in H-H. Second, we use existent (H-H) and
newly determined (H-He) accurate potentials and properties to provide a
theoretical investigation of the collisional effects on the blue wing of the
Lyman-alpha line of H perturbed by He and H. We study the relative
contributions in the blue wing of the H and He atoms according to their
relative densities. We finally achieve a comparison with recent COS
observations and propose an assignment for a feature centered at 1190 A.
