On the ambiguity of functions represented by divergent power series

Abstract

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.