Extrapolation of perturbation-theory expansions by self-similar   approximants
  The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures. 
S. Gluzman and V.I. Yukalov
math-ph cond-mat.stat-mech math.MP