SUMMATION OF ASYMPTOTIC EXPANSIONS OF MULTIPLE-VALUED FUNCTIONS USINGALGEBRAIC APPROXIMANTS - APPLICATION TO ANHARMONIC-OSCILLATORS

The divergent Rayleigh-Schrodinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pade approximants that are obtained from an algebraic equation of arbitrar y degree. Numerical results indicate that given enough terms in the as ymptotic expansion the rate of convergence of the diagonal staircase a pproximant sequence increases with the degree. Different branches of t he approximants converge to different branches of the function. The su ccess of the high-degree approximants is attributed to their ability t o model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large pert urbation parameter. An efficient recursive algorithm for computing the diagonal approximant sequence is presented.