Approximating Jones coefficients and other link invariants by Vassiliev   invariants
  We find approximations by Vassiliev invariants for the coefficients of the Jones polynomial and all specializations of the HOMFLY and Kauffman polynomials. Consequently, we obtain approximations of some other link invariants arising from the homology of branched covers of links. 
Ilya Kofman and Yongwu Rong