  Assuming the asymptotic character of divergent perturbation series, we
address the problem of ambiguity of a function determined by an asymptotic
power expansion. We consider functions represented by an integral of the
Laplace-Borel type, with a curvilinear integration contour. This paper is a
continuation of results recently obtained by us in a previous work. Our new
result contained in Lemma 3 of the present paper represents a further extension
of the class of contours of integration (and, by this, of the class of
functions possessing a given asymptotic expansion), allowing the curves to
intersect themselves or return back, closer to the origin. Estimates on the
remainders are obtained for different types of contours. Methods of reducing
the ambiguity by additional inputs are discussed using the particular case of
the Adler function in QCD.
