  Slowly convergent or divergent sequences and series occur abundantly in
quantum physics and quantum chemistry. These convergence problems can be
overcome with the help of nonlinear sequence transformations (Wynn's epsilon or
rho algorithm, Brezinski's theta algorithm, Levin's transformation, etc.) as
for instance described in E. J. Weniger, "Nonlinear sequence transformations
for the acceleration of convergence and the summation of divergent series",
Comput. Phys. Rep. Vol. 10, 189 - 371 (1989). A detailed description of the
mathematical properties of these transformations is given. The nonlinear
sequence transformations are applied for the evaluation of special or auxiliary
functions by summing divergent asymptotic expansions via rational approximants,
for the evaluation of complicated molecular multicenter integrals, for the
summation of the divergent perturbation expansions of the anharmonic
oscillators, or for the extrapolation of quantum chemical cluster calculations
on stereoregular quasi-one-dimensional polymers to the infinite chain limit.
