Maximum entropy summation of divergent perturbation series

In this paper the principle of maximum entropy is used to predict the sum of a divergent perturbation series from the first few expansion coefficients. The perturbation expansion for the ground-state energy E(g) of the octic oscillator defined by H=p2/2+x2/2+gx8 is a series of the form E(g)∼ 1/2 +∑(−1)n+1 Angn. This series is terribly divergent because for large n the perturbation coefficients An grow like (3n)!. This growth is so rapid that the solution to the moment problem is not unique and ordinary Padé summation of the divergent series fails. A completely different kind of procedure based on the principle of maximum entropy for reconstructing the function E(g) from its perturbation coefficients is presented. Very good numerical results are obtained.