  Recently the partial wave cutoff method was developed as a new calculational
scheme for a functional determinant of quantum field theory in radial
backgrounds. For the contribution given by an infinite sum of large partial
waves, we derive explicitly radial WKB series in the angular momentum cutoff
for $d=2,3,4$ and 5 ($d$ is the spacetime dimension), which has uniform
validity irrespectively of any specific values assumed for other parameters.
Utilizing this series, precision evaluation of the renormalized functional
determinant is possible with a relatively small number of low partial wave
contributions determined separately. We illustrate the power of this scheme in
numerically exact evaluation of the prefactor (expressed as a functional
determinant) in the case of the false vacuum decay of 4D scalar field theory.
