Analytic properties of Hansen coefficients |
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Authors: | Sergey Yu. Sadov |
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Affiliation: | (1) Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7 |
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Abstract: | Hansen’s coefficients in the theory of elliptic motion with eccentricity e are studied 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. |
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Keywords: | Two-body problem Elliptic motion Hansen coefficients High eccentricity Series expansion Analytic functions Poles and residues |
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