  In this paper, we consider the resummation of the divergent
Rayleigh-Shrodinger perturbation expansion for the ground state energy of the
quartic anharmonic oscillator in one dimension. We apply the Borel-Pade
resummation method combined with a conformal mapping of the Borel plane to
improve the accuracy and to enlarge the convergence domain of the perturbative
expansion. This technique was recently used in perturbative QCD to accelerate
the convergence of Borel-summed Green's functions. In this framework, we
calculated the ground state energy of the quartic anharmonic oscillator for
various coupling constants and compared our results with the ones we obtained
from the diagonal Pade approximation and the standard Borel resummation
technique. The results are also tested on a number of exact numerical solutions
available for weak and strong coupling constants. As a part of our
calculations, we computed the coefficients of the first 50 correction terms in
the Rayleigh-Shrodinger perturbation expansion using the method of Dalgarno and
Stewart. The conformal mapping of the Borel plane is shown to enhance the power
of Borel's method of summability, especially in the strong coupling domain
where perturbation theory is not applicable.
