LINK BETWEEN THE STRONG-COUPLING AND THE WEAK-COUPLING ASYMPTOTIC PERTURBATION EXPANSIONS FOR THE QUARTIC ANHARMONIC-OSCILLATOR

For eigenvalues E(beta) of the Hamiltonian of the quartic anharmonic o scillator we give a representation which reproduces two well known lim iting cases from the theory of the anharmonic oscillator expansions: t he weak-coupling asymptotic perturbation and the convergent strong cou pling. We give an estimation of the radius of convergence of the stron g-coupling expansion for the ground-state eigenvalue.