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Sine series expansion of associated Legendre functions

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Geodaetica et Geophysica" Springer Journals

Sine series expansion of associated Legendre functions

"Acta Geodaetica et Geophysica" , Volume 50 (2): 17 – Jun 1, 2015

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Publisher
Springer Journals
Copyright
2014 Akadémiai Kiadó
ISSN
2213-5812
eISSN
2213-5820
DOI
10.1007/s40328-014-0092-2
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

"Acta Geodaetica et Geophysica"Springer Journals

Published: Jun 1, 2015

References