Padé Approximants and Inner Projections in the Brillouin-Wigner Perturbation Scheme for He-like Ions

The continued-fraction expansions in terms of Brillouin-Wigner perturbation energies are evaluated for the He-like series. They show remarkable convergence and stability properties. Both Pad\'e approximants and perturbation energies are computed with formulas derived by the inner-projection technique.