Theorems on estimating perturbative coefficients in quantum field theory and statistical physics (Q1898830)

The authors start from a simple observation that the classical Padé approximant of a sufficiently high degree is exact when the approximated function is rational. Applying this fact to some series, they derive several trigonometric and other identities. Moreover, a sufficient condition for accuracy of estimation of the next term in a series expansion using the Padé approximation is established. These results are applied to hypergeometric series and to series from both perturbative quantum field theory and statistical physics. Results of several numerical experiments are also included.