  We derive simple new expressions, in various dimensions, for the functional
determinant of a radially separable partial differential operator, thereby
generalizing the one-dimensional result of Gel'fand and Yaglom to higher
dimensions. We use the zeta function formalism, and the results agree with what
one would obtain using the angular momentum cutoff method based on radial WKB.
The final expression is numerically equal to an alternative expression derived
in a Feynman diagrammatic approach, but is considerably simpler.
