  Gell-Mann-Low functions can be calculated by means of perturbation theory and
expressed as truncated series in powers of asymptotically small coupling
parameters. However, it is necessary to know there behavior at finite values of
the parameter and, moreover, their behavior at asymptotically large coupling
parameters is also important. The problem of extrapolation of weak-coupling
expansions to the region of finite and even infinite coupling parameters is
considered. A method is suggested allowing for such an extrapolation. The
basics of the method are described and illustrations of its applications are
given for the examples where its accuracy and convergence can be checked. It is
shown that in some cases the method allows for the exact reconstruction of the
whole functions from their weak-coupling asymptotic expansions. Gell-Mann-Low
functions in multicomponent field theory, quantum electrodynamics, and quantum
chromodynamics are extrapolated to their strong-coupling limits.
