Show simple item record

dc.contributor.authorClaessens, Sten
dc.identifier.citationClaessens, Sten. 2005. New Relations Among Associated Legendre Functions and Spherical Harmonics. Journal of Geodesy 79 (6-7): 398-406.

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.publisherSpringer - Verlag
dc.subjectSpherical Harmonics
dc.subjectAssociated Legendre Functions
dc.titleNew Relations Among Associated Legendre Functions and Spherical Harmonics
dc.typeJournal Article
dcterms.source.titleJournal of Geodesy

The original publication is available at

curtin.accessStatusOpen access
curtin.facultyDivision of Resources and Environment
curtin.facultyDepartment of Spatial Sciences

Files in this item


This item appears in the following Collection(s)

Show simple item record