RECONSTRUCTION OF THE EXACT GROUND-STATE ENERGY OF THE QUARTIC ANHARMONIC-OSCILLATOR FROM THE COEFFICIENTS OF ITS DIVERGENT PERTURBATION EXPANSION

We present a method of the summation of the divergent series. We show that in the case of the divergent perturbation expansion for the quart ic anharmonic oscillator, the method allows one to construct the seque nce of the analytic approximations to the E(beta) exact ground-state e nergy. The constructed sequence converges for any value of the couplin g constant beta, allowing one to reconstruct the function E(beta) in a whole beta plane.