Abstract The most regularly used mathematical tools for representing the geopotential globally are the spherical harmonics, which consists of the longitude-dependent Fourier transform and of the latitude-dependent associated Legendre functions. While the former is by definition a Fourier series, the latter also can be formed to that. An alternative formulation for the sine series expansion of associated Legendre polynomials has been derived based on well-known recurrence formulae. The resulted formulae are subsequently empirically tested for errors to determine the limitations of its use, and strong dependence on the co-latitude has been found.
"Acta Geodaetica et Geophysica" – Springer Journals
Published: Jun 1, 2015