Generalized moments applied to Fermi‐type functions

Generalized integral moments are defined for a general class of saturating functions [ f(0)=ρ0, f(∞)=0]. They are useful as independent variables for describing surface properties or macroscopic dynamics of finite systems. Applied especially to functions of the Fermi type, analytic solutions are given in terms of a semiconverging, and of a numerically semiunstable expansion, respectively, suitable for numerical evaluation. Results are compared to the semidivergent expansion as given by Åberg, of which some properties are exhibited here, and with the exact numerical solutions known for this special example.