A new method for summation of divergent power series

Abstract

A new method for summation of divergent power series is developed. It only requires the knowledge of the form of both the small and large λ-power expansion (λ being the perturbation parameter) and few coefficients of one of them to yield excellent results. Convergence is proved for a simple two-level model, and reasonable arguments are given for more complex and interesting models. The method is quite general and contains some resummation techniques reported previously as particular cases. The anharmonic, mean square, displacement function, the ground-state eigenvalue of the quantum-mechanical anharmonic oscillator, and the ground-state energy of the hydrogen atom in a magnetic field calculated in this way are shown to be of striking accuracy in the whole range of the perturbation parameter.