Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$

It is considered what new has been achieved by the progress in many-loop calculations and the method of asymptotic estimates of the perturbation series coefficients in the elucidation of the physical situation with regard to the behavior of the effective charg at short distances. The treatment is given for the example of the theory $\varphi^4_{(4)}$. A procedure is proposed for constructing approximants of the Gell-Mann–Low function on the basis of a synthesis of the exact coefficients of the lowest orders and asymptotic estimates in the integral representation. It is shown that in the $g\varphi^4$ model the Gell-Mann–Low function has behavior of the type $0{,}9\,g^2$ for $g\gtrsim1$.