Note on the generalized Hansen and Laplace coefficients

Abstract

Recently, Breiter et al (2004) 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) that do not require $s,r$ to be integers. In particular, the coefficients $X_0^{\g,m}$ have very simple expressions in terms of the usual Laplace coefficients $b_{\g+2}^{(m)}$, and all their properties derive easily from the known properties of the Laplace coefficients.