A New Normalization Form Based on a General Unified Normalization Computing for the Gravitational Potential Tensor of Arbitrary Orders

Abstract

Taking a general unified recursive algorithm for computing the normalized gravitational potential based on Cunningham's formula into account, the numerical stability of both the recursion for spherical harmonic series and the pre-processing for the spherical harmonic coefficients are discussed. Then a new method of normalizing the associated Legendre polynomial is proposed.