  We investigate some properties of the WKB series for arbitrary analytic
potentials and then specifically for potentials $x^N$ ($N$ even), where more
explicit formulae for the WKB terms are derived. Our main new results are: (i)
We find the explicit functional form for the general WKB terms $\sigma_k'$,
where one has only to solve a general recursion relation for the rational
coefficients. (ii) We give a systematic algorithm for a dramatic simplification
of the integrated WKB terms $\oint \sigma_k'dx$ that enter the energy
eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms
for the energy eigenvalues of the homogeneous power law potentials $V(x) =
x^N$, where $N$ is even. In particular, we obtain effective algorithms to
compute and reduce the terms of these series.
