Analytic properties of Hansen coefficientsстатьяИсследовательская статья
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Аннотация:Hansen’s coefficients in the theory of elliptic motion with eccentricity e arestudied as functions of the parameter η = (1−e^2)^(1/2). Their analytic behavior in the complex η plane is described and some symmetry relations are derived. In particular, for every Hansen coefficient, multiplication by suitable powers of e and η results in an entire analytic function of η. Consequently, Hansen’s coefficients can be in principle computed by means of rapidly convergent series in powers of η. A representation of Hansen’s coefficients in terms of two entire functions of e^2 follows.