  We obtain the rigorous WKB expansion to all orders for the radial Kepler
problem, using the residue calculus in evaluating the WKB quantization
condition in terms of a complex contour integral in the complexified coordinate
plane. The procedure yields the exact energy spectrum of this Schr\"odinger
eigenvalue problem and thus resolves the controversies around the so-called
"Langer correction". The problem is nontrivial also because there are only a
few systems for which all orders of the WKB series can be calculated, yielding
a convergent series whose sum is equal to the exact result, and thus sheds new
light to similar and more difficult problems.
