Perturbation Theory with Convergent Series for Large Values of Coupling Constant:. a Calculation of β-FUNCTION in φ4 Model

A new perturbation theory with convergent series is used to calculate quantities given by a finite number of terms of the traditional perturbation theory. As examples of such a problem, the zero-dimensional analog of a functional integral and β-function in gφ⁴ model in four-dimensional space-time are considered. The results obtained demonstrate high accuracy of the calculation in a wide region of coupling constant values.