| 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 |
| Genre: | Article |
| ProdID: | 70014881 |
| Citation Author: | Alldredge, L. R.; Benton, E. R. |
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| Citation End Page: | 609 |
| Citation Issue: | 6 |
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| Citation Language: | English |
| Citation Larger Work Title: | Journal of Geomagnetism & Geoelectricity |
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| Citation Number Of Pages: | 11 |
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| Citation Search Results Text: | Alternate forms of the associated Legendre functions for use in geomagnetic modeling.; 1986; Article; Journal; Journal of Geomagnetism & Geoelectricity; Alldredge, L. R.; Benton, E. R. |
| Citation Start Page: | 599 |
| Citation Volume: | 38 |
| Citation Year: | 1986 |
| Type: | citation/reference |
| Text: | Alternate forms of the associated Legendre functions for use in geomagnetic modeling.; 1986; Article; Journal; Journal of Geomagnetism & Geoelectricity; Alldredge, L. R.; Benton, E. R. |
| URL (THUMBNAIL): | http://pubs.er.usgs.gov/thumbnails/outside_thumb.jpg |
| Date Other: | Wed, 1 Jan 1986 00:00 -0600 |
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