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Sine series expansion of associated Legendre functions

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.

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Acknowledgments

This study was supported by the OTKA Fund, Project Number K106118.

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Correspondence to Lóránt Földváry.

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Földváry, L. Sine series expansion of associated Legendre functions. Acta Geod Geophys 50, 243–259 (2015). https://doi.org/10.1007/s40328-014-0092-2

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  • DOI: https://doi.org/10.1007/s40328-014-0092-2

Keywords

  • Sine series expansion
  • Associated Legendre functions
  • Spherical harmonics