Recurrence formulae for the Hansen's developments

In this paper we derive some recurrence formulae which can be used to calculate the Fourier expansions of the functions (r/a) ⁿ cosmv and (r/a) ⁿ sinmv in terms of the eccentric anomalyE or the mean anomalyM. We also establish a recurrence process for computing the series expansions for alln andm when the expansions of two basic series are known. These basic series were given in explicit form in the classical literature. The recurrence formulae are linear in the functions involved and thus make very simple the computation of the series.This work was supported by NASA contract No. NASr 54(06).—The paper was presented at the AIAA/AAS meeting, Princeton University, August 1969.