Analytic properties of Hansen coefficients

Details Analytic properties of Hansen coefficients Analytic properties of Hansen coefficients

Apr 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cemda.100..287s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 100, Issue 4, pp.287-300

Astronomy and Astrophysics

Astronomy

2

Scientific paper

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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