Darboux functions and power series expansions with examples from isoelectronic sequences

A procedure for summing a power series based on a Darboux function ansatz is developed. It involves computation of poles and residues of logarithmic derivatives using rational functions. Applications to the helium isoelectronic sequence condense the power series expansion (˜ 40 coefficients) to a few-parameter formula, which exhibits the singularity determining the radius of convergence. Accurate extrapolations of electron affinities and shielding factors are obtained.