Construction of polynomial approximation for Hansen coefficients

The problem of constructing efficient approximations of Hansen coefficients using polynomials in terms of the eccentricity is considered. The properti es of the following approximating schemes are studied in detail: approximat ion by fragments of Taylor series, interpolation by Lagrange polynomials, C hebyshev approximation. The accuracy of all these approximating schemes is investigated for different values of eccentricities and for different indic es of the Hansen coefficients. (C) 2000 Elsevier Science B.V. All rights re served.