  The spectral problem for O(D) symmetric polynomial potentials allows for a
partial algebraic solution after analytical continuation to negative even
dimensions D. This fact is closely related to the disappearance of the
factorial growth of large orders of the perturbation theory at negative even D.
As a consequence, certain quantities constructed from the perturbative
coefficients exhibit fast inverse factorial convergence to the asymptotic
values in the limit of large orders. This quantum mechanical construction can
be generalized to the case of quantum field theory.
