Asymptotic estimates and borel resummation for a doubly anharmonic oscillator

The large-order behavior of perturbation theory for an oscillator with both quartic and sextic anharmonicity is examined. Two approaches are considered: an explicit double expansion in the two coupling constants and a single expansion in the number of loops. A two-variable extension of the Borel resummation technique is developed and applied to the double series, and the standard one-variable resummation technique is applied to the loop expansion. Numerical values for the ground-state energy are calculated in each case and the two procedures are compared.