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In this paper, we consider the resummation of the divergentRayleigh-Shrodinger perturbation expansion for the ground state energy of thequartic anharmonic oscillator in one dimension. We apply the Borel-Paderesummation method combined with a conformal mapping of the Borel plane toimprove the accuracy and to enlarge the convergence domain of the perturbativeexpansion. This technique was recently used in perturbative QCD to acceleratethe convergence of Borel-summed Green's functions. In this framework, wecalculated the ground state energy of the quartic anharmonic oscillator forvarious coupling constants and compared our results with the ones we obtainedfrom the diagonal Pade approximation and the standard Borel resummationtechnique. The results are also tested on a number of exact numerical solutionsavailable for weak and strong coupling constants. As a part of ourcalculations, we computed the coefficients of the first 50 correction terms inthe Rayleigh-Shrodinger perturbation expansion using the method of Dalgarno andStewart. The conformal mapping of the Borel plane is shown to enhance the powerof Borel's method of summability, especially in the strong coupling domainwhere perturbation theory is not applicable.

Borel Resummation Method with Conformal Mapping and the Ground State Energy of the Quartic Anharmonic Oscillator