Borel summation of divergent series in field theory and Wynn's element of algorithm

The first confluent form of Wynn's element of algorithm is used in the Borel summation of some divergent perturbation-theory series that satisfy a strong asymptotic condition. The summation procedure reduces to the calculation of a sequence of ratios of Hankel functional determinants composed of a Borel integral and its derivatives and can be regarded as an alternative to the Pade and Pade-Borel methods. It admits a simple generalization to the summation of multiple series. The perturbation series for the ground-state energy of the anharmonic oscillator, Yukawa potential, and charmonium potential are analyzed; the critical exponents of the O(n)-symmetric Phi4 theories (models of phase transitions) for n = 0, 1, 2, 3 and the dilute Ising model are determined