Alternate forms of the associated Legendre functions for use in geomagnetic modeling.
Journal of Geomagnetism & Geoelectricity
By: L.R. Alldredge and E.R. Benton
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Abstract
An inconvenience attending traditional use of associated Legendre functions in global modeling is that the functions are not separable with respect to the 2 indices (order and degree). In 1973 Merilees suggested a way to avoid the problem by showing that associated Legendre functions of order m and degree m+k can be expressed in terms of elementary functions. This note calls attention to some possible gains in time savings and accuracy in geomagnetic modeling based upon this form. For this purpose, expansions of associated Legendre polynomials in terms of sines and cosines of multiple angles are displayed up to degree and order 10. Examples are also given explaining how some surface spherical harmonics can be transformed into true Fourier series for selected polar great circle paths. -from Authors
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Alternate forms of the associated Legendre functions for use in geomagnetic modeling. |
| Series title | Journal of Geomagnetism & Geoelectricity |
| Volume | 38 |
| Issue | 6 |
| Year Published | 1986 |
| Language | English |
| Larger Work Type | Article |
| Larger Work Subtype | Journal Article |
| Larger Work Title | Journal of Geomagnetism & Geoelectricity |
| First page | 599 |
| Last page | 609 |
| Google Analytic Metrics | Metrics page |