We consider a vectorial, asymptotically free SU(Nc) gauge theory with Nf fermions in a representation R having an infrared (IR) fixed point. We calculate and analyze Padé approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, γψψ,IR, to O(Δf4), and the derivative of the beta function, βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of γψψ,IR and βIR′ for several SU(Nc) groups and representations R, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For R=F, the limit Nc→âž and Nf→âž with Nf/Nc fixed is considered. We assess the accuracy of the scheme-independent series expansion of γψψ,IR in comparison with the exactly known expression in an N=1 supersymmetric gauge theory. It is shown that an expansion of γψψ,IR to O(Δf4) is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.