DETERMINATION OF F(INFINITY) FROM THE ASYMPTOTIC SERIES FOR F(X) ABOUT X=0

A difficult and long-standing problem in mathematical physics concerns the determination of the value of f(infinity) from the asymptotic series for f(x) about x = 0. In the past the approach has been to convert the asymptotic series to a sequence of Pade approximants {P(n)n(x)} and then to evaluate these approximants at x= infinity. Unfortunately, for most physical applications the sequence {P(n)n(infinity)} is slowly converging and does not usually give very accurate results. In this paper the results of extensive numerical studies for a large class of functions f(x) associated with strong-coupling lattice approximations are reported. It is conjectured that for large n, P(n)n(infinity) is similar to f(infinity) + B/ln n. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of f(infinity).