Calculating $\beta$-function in the $\varphi^4$-model in a wide range of coupling constant values

In the framework of a new theory of perturbations with converging series, a problem is considered of reconstructing the quantity defined by a finite number of its perturbative expansion terms in a wide range of coupling constant values. As exam.pies of such problems, we consider a zero-dimensional analog of a functional integral and a $\beta$-function of the $g(\varphi^a\varphi^a)^2$ model ($a=1,2,$) in the four-dimensional space-time.