dc.contributor.author Claessens, Sten dc.date.accessioned 2017-01-30T12:13:57Z dc.date.available 2017-01-30T12:13:57Z dc.date.created 2008-11-12T23:36:45Z dc.date.issued 2005 dc.identifier.citation Claessens, Sten. 2005. New Relations Among Associated Legendre Functions and Spherical Harmonics. Journal of Geodesy 79 (6-7): 398-406. dc.identifier.uri http://hdl.handle.net/20.500.11937/19446 dc.identifier.doi 10.1007/s00190-005-0483-9 dc.description.abstract Several new relations among associated Legendre functions (ALFs) are derived, most of which relate a product of an ALF with trigonometric functions to a weighted summation over ALFs, where the weights only depend on the degree and order of the ALF. These relations are, for example, useful in applications such as the computation of geopotential coefficients and computation of ellipsoidal corrections in geoid modelling. The main relations are presented in both their unnormalised and fully normalised ($4\pi$-normalised) form. Several approaches to compute the weights involved are discussed, and it is shown that the relations can also be applied in the case of first- and second-order derivatives of ALFs, which may be of use in analysis of satellite gradiometry data. Finally, the derived relations are combined to provide new identities among ALFs, which contain no dependency on the colatitudinal coordinate other than that in the ALFs themselves. dc.publisher Springer - Verlag dc.subject Spherical Harmonics dc.subject Associated Legendre Functions dc.title New Relations Among Associated Legendre Functions and Spherical Harmonics dc.type Journal Article dcterms.source.volume 79 dcterms.source.number 6-7 dcterms.source.startPage 398 dcterms.source.endPage 406 dcterms.source.title Journal of Geodesy curtin.note The original publication is available at https://link.springer.com/ curtin.identifier EPR-3175 curtin.accessStatus Open access curtin.faculty Division of Resources and Environment curtin.faculty Department of Spatial Sciences
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