Solving the Stieltjes summation problem by finite part integration

Abstract

Using finite part integration, we were able obtain a solution to the Stieltjes summation problem. The prescription consisted of reconstructing a function from a finite string of moments. This reconstruction is then used in the expansion of the Stieltjes integral by finite part integration to obtain meaningful values of otherwise divergent Stieltjes series. The prescription is then applied to the eigenvalue problem of the quartic anharmonic oscillator which showed remarkable accuracy for obtaining the ground-state energy eigenvalues from the Rayleigh-Schrodinger perturbation series.