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Sine series expansion of associated Legendre functions

Acta Geodaetica et Geophysica volume 50, pages 243–259 (2015)Cite this article

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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Authors and Affiliations

  1. Department of Geodesy and Surveying, Budapest University of Technology and Economics, Műegyetem rkp 3, H-1111, Budapest, Hungary

    Lóránt Földváry

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  1. Lóránt Földváry
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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