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    New Relations Among Associated Legendre Functions and Spherical Harmonics

    21041_downloaded_stream_497.pdf (136.1Kb)
    Access Status
    Open access
    Authors
    Claessens, Sten
    Date
    2005
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Claessens, Sten. 2005. New Relations Among Associated Legendre Functions and Spherical Harmonics. Journal of Geodesy 79 (6-7): 398-406.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-005-0483-9
    Faculty
    Division of Resources and Environment
    Department of Spatial Sciences
    Remarks

    The original publication is available at https://link.springer.com/

    URI
    http://hdl.handle.net/20.500.11937/19446
    Collection
    • Curtin Research Publications
    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.

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