The strongly divergent Rayleigh-Schrodinger perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator and a corresponding renormalized perturbation expansion [F. Vinette and J. Cizek, J. Math. Phys. 32, 3392 (1991)] are summed by Pade approximants, by Levin's sequence transformation [D. Levin, Int. J. Comput. Math. B 3, 371 (1973)], and by a closely related sequence transformation which was suggested recently [E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989)]. It is shown that the renormalized perturbation expansion can be summed much more easily than the original perturbation expansion from which it was derived, and that Levin's sequence transformation diverges and is not able to sum the perturbation expansions. The Pade summation of the renormalized perturbation expansions gives relatively good results in the quartic and sextic case. In the case of the octic anharmonic oscillator, even the renormalized perturbation expansion is not Pade summable. The best results are clearly obtained by the new sequence transformation which, for instance, is able to sum the renormalized perturbation expansions for the infinite coupling limits of the quartic, sextic, and octic anharmonic oscillator, and which produces at least in the quartic and sextic case extremely accurate results.
