Transformation of the asymptotic perturbation expansion for the anharmonic oscillator into a convergent expansion

For eigenvalues E(beta) of, the Hamiltonian of the quartic anharmonic oscillator we give a procedure allowing to transform the asymptotic Rayleigh-Schrodinger perturbation expansion into a convergent expansion, coefficients of the latter expansion being given explicitly as some linear combinations of the coefficients of the perturbation expansion. 2004 Elsevier B.V. All rights reserved.