Multipolar expansions arise in many branches of the
computational sciences. They are an example of orthogonal expansions.
We present methods for the convergence acceleration of such
expansions. As an example, the computation of the electrostatic potential and its multipolar expansion is treated for the case of a two-center charge
density of exponential-type orbitals. This potential may also be considered as
a special molecular integral, namely as a three-center nuclear attraction
integral. It is shown that in this example, the extrapolation to the limit of the
corresponding expansions via suitable nonlinear sequence transformations leads
to a pronounced convergence acceleration.