  The previously obtained analytical asymptotic expressions for the Gell-Mann -
Low function \beta(g) and anomalous dimensions of \phi^4 theory in the limit
g\to\infty are based on the parametric representation of the form g = f(t),
\beta(g) = f1(t) (where t\sim g_0^{-1/2} is the running parameter related to
the bare charge g_0), which is simplified in the complex t plane near a zero of
one of the functional integrals. In the present paper, it is shown that the
parametric representation has a singularity at t\to 0; for this reason, similar
results can be obtained for real values of g_0. The problem of the correct
transition to the strong coupling regime is simultaneously solved; in
particular, the constancy of the bare or renormalized mass is not a correct
condition of this transition. A partial proof is given for the theorem of the
renormalizability in the strong coupling region.
