Summary: Situations arise in celestial mechanics where orbital eccentricities are large and yet it is desirable to maintain the Darwin-Kaula Fourier decomposition of the perturbing function. Evaluation of the appropriate eccentricity functions \(G_{lpq}(e)\) requires a double summation which, for practical purposes, must be truncated. In this note criteria have been established for truncation of the expansion for eccentricities \(\leq 0.75\).