Note on the Generalized Hansen and Laplace Coefficients

Abstract

Recently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153–161] reported the computation of Hansen coefficients X ^{γ ,m} _k for non-integer values of γ. 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 ^{γ ,m}₀ have very simple expressions in terms of the usual Laplace coefficients b _{γ +2} ^(m), and all their properties derive easily from the known properties of the Laplace coefficients.