New Relations Among Associated Legendre Functions and Spherical Harmonics
MetadataShow full item record
The original publication is available at https://link.springer.com/
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.
Showing items related by title, author, creator and subject.
Turner, Sian Elizabeth (2009)Background and research questions. The characterization of chronic persistent asthma in an older adult population is not well defined. This is due to the difficulties in separating the diagnosis of asthma from that of ...
Alchin, Mark David (2011)Australia’s rangelands encompass approximately 80% of the continent and generate significant wealth through a range of industries. The rangelands comprise four major ecosystem types, these are: grasslands, shrublands, ...
Coming of age in the digital era: An exploratory transnational study into Australian and Singaporean PR consultants’ attitude towards digital communication.Archer, C.; Wolf, Katharina (2017)Digital and social media tools are no longer new and have become standard components of the public relations toolkit. However, they have undoubtedly changed and shaped the practice of public relations (PR) over the past ...