Note on the Generalized Hansen and Laplace Coefficients

International audienceRecently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153 161] reported the computation of Hansen coefficients X k gamma ,m for non-integer values of gamma. In fact, the Hansen coefficients are closely related to the Laplace b s (m), and generalized Laplace coefficients b s,r (m) [Laskar and Robutel, 1995, Celest. Mech. Dyn. Astron., 62, 193 217] that do not require s,r to be integers. In particular, the coefficients X 0 gamma ,m have very simple expressions in terms of the usual Laplace coefficients b gamma +2 (m), and all their properties derive easily from the known properties of the Laplace coefficients