We demonstrate that it is possible to determine the coefficients of an all-order beta function linear in the anomalous dimensions using as data the two-loop coefficients together with the first one of the anomalous dimensions which are universal. The beta function allows to determine the anomalous dimension of the fermion masses at the infrared fixed point, and the resulting values compare well with the lattice determinations.

Version to match the published one in Phys. Rev. D. We added several tables demonstrating how well the prediction for the anomalous dimensions at the fixed point obtained via the all-orders beta function compares with the one obtained in perturbation theory. We added also a figure