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The previous attempts of reconstructing the Gell-Mann-Low function \beta(g)of the \phi^4 theory by summing perturbation series give the asymptoticbehavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where\alpha \approx 1 for the space dimensions d = 2,3,4. It can be hypothesizedthat the asymptotic behavior is \beta(g) ~ g for all values of d. Theconsideration of the zero-dimensional case supports this hypothesis and revealsthe mechanism of its appearance: it is associated with a zero of one of thefunctional integrals. The generalization of the analysis confirms theasymptotic behavior \beta(g)=\beta_\infty g in the general d-dimensional case.The asymptotic behavior of other renormalization group functions is constant.The connection with the zero-charge problem and triviality of the \phi^4 theoryis discussed.

Renormalization Group Functions of the \phi^4 Theory in the Strong Coupling Limit: Analytical Results