Abstract
The properties of a generalized version of the Borel transform in infrared unstable theories wth dynamical mass generation are studied. The reconstruction of the nonperturbative structure is unambiguous in this version. Various methods for extracting the singularity structure of the Borel transform for lattice formulations of such theories are explored and illustrated explicitly with the O(N) \ensuremath{\sigma} model. The status of the first infrared renormalon in QCD is discussed. The feasibility of a proposed technique for analytically continuing from the left-hand Borel plane (where nonperturbative information is available via simulation of lattice field theory) to the positive real axis is examined using the \ensuremath{\sigma} model.
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