Estimating perturbative coefficients in quantum field theory using Padé approximants

We show how one can accelerate the convergence of a perturbation series by using Padé approximants. We use the first few coefficients of each perturbation series to predict the next term. We first check our method for known results and then predict the value of, as yet, unknown terms. Our results for $a_{\mu }-a_e$, $a_e$, $a_{\mu }$, $R_{\tau }$, and the QCD $\beta$ function are remarkably good.