The expansion of the potential of a homogeneous ellipsoid in a series of tesseral harmonics

The Newtonian potential of a homogeneous triaxial ellipsoid is expanded in a series of tesseral harmonics (cf. Equation (1)) and the coefficients (cf. Equation (2)) are calculated (cf. Equation (25)). An integral formula of Legendre involving Legendre polynomials is generalized to associated Legendre functions (cf. Equation (16), (16^*)).